6 Gradiente Boosting

Assim como a Floresta Aleatória de Breiman (Breiman 2001), o Gradiente Boosting de Friedman (Friedman 2001) é um método para dados supervisionados que combina muitas árvores para gerar uma única previsão. Mas a maneira que as árvores são construídas e a previsão final são bem diferentes entre os dois métodos.

Como já visto no capítulo anterior, a Floresta Aleatória é um método de aprendizagem de conjunto (ensemble learning) que combina várias árvores de decisão para fazer previsões. Cada árvore de decisão é treinada em uma amostra aleatória do conjunto de dados, usando a técnica bootstrapping (amostragem com reposição). Além disso, em cada divisão de uma árvore de decisão da floresta, apenas um subconjunto aleatório de variáveis é considerado para escolher a melhor divisão. No final, as previsões de cada árvore são combinadas para se obter a previsão final.

Podemos dizer que as árvores da Floresta Aleatória são construídas “em paralelo”, são árvores independentes e as previsões de todas elas, que podem ser feitas ao mesmo tempo, resulta no modelo final. Já o Boosting constrói as árvores “em série”, de forma sequencial. Cada nova árvore é treinada para corrigir os erros cometidos pelas árvores anteriores. As árvores não são independentes e o resultado final precisa passar por cada uma das árvores, na ordem em que elas foram construídas, para ser obtido.

6.1 Boosting

Os métodos de aprendizado Boosting são uma classe de algoritmos de aprendizado de máquina que combinam vários modelos fracos para formar um modelo forte e de alta precisão. A ideia central do Boosting é treinar os modelos de forma sequencial, onde cada novo modelo é construído para corrigir os erros cometidos pelos modelos anteriores.

O Boosting é conhecido por sua capacidade de melhorar gradualmente a precisão do modelo à medida que novos modelos são adicionados. Ele é especialmente eficaz em problemas complexos e difíceis, onde um único modelo fraco não é suficiente para obter um bom desempenho.

6.2 O Método

De forma bem geral, o Gradiente Boosting começa com um primeiro método de aprendizado bem simples, conhecido como aprendizado fraco. Este método pode ser uma árvore com uma única partição ou até mesmo a média amostral, para o caso de regressão, ou a proporção das classes, para o caso de classificação. vamos chamar o aprendizado fraco de \(A_0\), que retorna uma previsão para cada observação \(\mathbf{x}_i\), denominado \(A_0(\mathbf{x}_i)\). Considerando o método apenas com o aprendizado fraco, a previsão para o observação \(\mathbf{x}_i\) será dada por:

\[F_0(\mathbf{x}_i) = A_0(\mathbf{x}_i)\] sendo \(F_0(\mathbf{x}_i)\) a previsão do Gradiente Boosting para a observação \(\mathbf{x}_i\) no momento inicial.

Em seguida são calculados os erros cometidos na base de treino. Chama-se \(e^0_i\) o erro da observação \(i\) no momento inicial do método.

\[ e^0_i = y_i - F_0(\mathbf{x}_i) \]

Uma nova árvore é ajustada, mas agora a variável resposta é o erro \(\mathbf{e^0}\). Vamos chamar essa árvore de \(A_1\), que é a primeira árvore construída para prever o erro. Denomina-se \(A_1(\mathbf{x}_i)\) a previsão dada por \(A_1\) para cada observação \(\mathbf{x}_i\). Com estas duas árvores o método fornece como previsão para a observação \(\mathbf{x}_i\)

\[ F_1(\mathbf{x}_i) = F_0(\mathbf{x}_i) + A_1(\mathbf{x}_i) \]

Sendo \(F_1(\mathbf{x}_i)\) a previsão dada pelo Gradiente Boosting na primeira iteração. Novamente é encontrado o erro cometido pelo método:

\[ e^1_i = y_i - F_1(\mathbf{x}_i). \] O erro sempre será a diferença entre o valor observado e o valor previsto pela última iteração do método. Mais uma árvore é ajustada, agora para prever os erros \(\mathbf{e^1}\). O processo é repetido até que se tenha construído as \(M\) árvores previstas pelo algoritmo.

Veja que é sempre possível escrever a previsão do método na iteração \(m\) em termos da sua previsão na iteração anterior:

\[ F_m(\mathbf{x}_i) = F_{m-1}(\mathbf{x}_i) + A_m(\mathbf{x}_i) \]

6.3 Regularização

A maior preocupação ao construir um modelo de aprendizado de máquina a partir de dados é a capacidade de generalização do modelo. Se o algoritmo de aprendizado não for aplicado corretamente, o modelo pode facilmente superajustar os dados. Esta também é uma preocupação para o método do Gradiente Boosting (Natekin and Knoll 2013).

6.3.1 Subamostragem

A técnicas mais simples de regularização é a subamostragem. A ideia é introduzir algum grau de aleatoriedade no procedimento de ajuste. Para isso, para cada árvore construída apenas uma parte aleatória dos dados de treinamento é usada, normalmente os dados de treinamento são amostrados sem reposição.

Esta etapa gera um hiperparâmetro chamado de “fração de amostragem” (bag. fraction), que especifica a proporção dos dados a serem usados em cada iteração. Por exemplo, \(\lambda = 0,1\) corresponde a usar 10% dos dados em cada iteração para o ajuste de cada árvore. Constuma-se usar \(\lambda=0,5\), mas o valor ideal para este parãmetro pode ser definido a partir de uma validação cruzada. Uma propriedade útil do subsampling é que ele se adapta naturalmente aos conjuntos grandes de dados, quando não há razão para usar todas as enormes quantidades de dados de uma só vez.

6.3.2 Taxa de Aprendizagem (shrinkage)

A abordagem clássica para controlar a complexidade do modelo é a introdução de uma taxa de aprendizado \(\nu \in (0,1]\). Esta taxa é usada para reduzir o impacto das correções dos erros e reduzir o tamanho dos passos incrementais em cada etapa. A intuição por trás dessa técnica é: chegamos à um resultado melhor com muitos pequenos passos do que com poucos grandes passos. Além disso, se uma das iterações se mostrar errônea, seu impacto negativo pode ser facilmente corrigido em etapas subsequentes.

\[ F_m(\mathbf{x}_i) = F_{m-1}(\mathbf{x}_i) + \nu A_m(\mathbf{x}_i) \]

6.4 Regressão x Classificação

Parece natural pensar no Gradiente Boosting para Regressão: temos árvores de regressão em sequência onde cada uma conserta o erro, que é um valor numérico contínua, da etapa anterior. E para o caso da classificação? O que seria o erro que será usado como variável alvo na etapa seguinte?

No método Gradient Boosting para classificação o modelo de aprendizado fraco, \(A_0\), será um modelo de classificação que retorna como previsão um número entre 0 e 1, que indica a chance da classe referência ser a classe escolhida. O erro então é calculado como a diferença entre a previsão dada por \(A_0\) e o valor de variável indicadora que representa a classe. Assim se \(A_0 \approx 1\) e a classe referência for a verdadeira, o erro será pequeno. Por outro lado, se \(A_0 \approx 1\) e a classe referência for falsa, o erro será grande.

No momento da construção de \(A_1\), a primeira árvore de correção dos erros, a variável alvo não será mais uma categoria e sim um valor contínuo que indica o erro. Daí por diante todas as árvores construídas pelo método são de regressão, mesmo o método sendo para classificação.

No entanto, é importante observar que, apesar de usar árvores de regressão para corrigir os erros, o Gradient Boosting é amplamente utilizado para problemas de classificação, onde o objetivo é prever rótulos de classe discretos. Isso é possível porque, após a etapa de treinamento do Gradient Boosting, a combinação das previsões de todas as árvores é usada para atribuir à cada instâncias um valor entre 0 e 1 que indica a classe prevista.

6.5 Algoritmo

Considere uma base de dados supervisionada, onde \(Y\) é a variável resposta (qualitativa ou quantitativa) e \(X_j\), \(j=1, 2, \ldots, p\) são as \(p\) covariáveis. Para cada observação \(i\), \(i=1, 2, \ldots, n\), isto é, para cada linha \(i\) da base, temos \(Y_i\) o valor da variável resposta para a observação \(i\) e \(X_{i,j}\) o valor ca covariável \(j\) para a observação \(i\). Posto isso, segue o algoritmo para o Método de Floresta Aleatória.

Escolhem-se os valores para os hiperparâmetros \(\lambda\), \(M\) e \(\nu\).

Ajuste o modelo fraco \(A_0\): \(F(\mathbf{x}_i) = A_0(\mathbf{x}_i)\).
Faça \(m=1\).
Calcule os erros \(e_i = y_i - F(\mathbf{x}_i)\).
Faça uma seleção aleatória simples, sem reposição, de \(\lambda \times 100\%\) da base de treino.
Ajuste uma árvore de regressão \(A_m\) para prever os erros \(e_i\) usando como base de treino o sorteio da etapa anterior.
Atualize: \(F(\mathbf{x}_i) = F(\mathbf{x}_i) + \nu A_m(\mathbf{x}_i)\).
Se \(m<M\), volte para o passo 3.

6.6 XGBoost

O XGBoost (Extreme Gradient Boosting) é uma implementação otimizada e aprimorada do algoritmo de gradiente boosting. o XGBoost também é baseado em um conjunto de árvores de decisão onde cada árvore é construída sequencialmente, corrigindo os erros residuais das árvores anteriores. Ele foi projetado para ser mais eficiente, rápido e preciso em comparação com outras implementações de gradient boosting.

6.6.1 Melhorias na Regularização

O XGBoost incorpora técnicas avançadas de regularização para evitar o overfitting e melhorar a capacidade de generalização do modelo. Isso inclui a adição de termos de penalidade nas funções de perda e a utilização de técnicas como a poda de árvores para evitar o crescimento excessivo.

Enquanto para o gradiente boosting a função de perda geralmente é o erro quadrático médio, \[ MSE = \dfrac{1}{n} \sum_{i=1}^n \left( y_i - \hat{y}_i\right)^2 \] ou seja, em cada partição de cada árvore busca-se a variável que minimiza o MSE, para XGBoost a função de perda recebe um termo de regularização, que controla a complexidade do modelo e penalizando árvores mais complexas

Melhorias no tempo de execução: O XGBoost utiliza técnicas eficientes de otimização para melhorar o desempenho do modelo. Isso inclui amostragem estocástica de dados durante o treinamento e a aplicação de algoritmos de aproximação para acelerar o processo de ajuste dos parâmetros. O XGBoost também possui a capacidade de paralelizar o treinamento das árvores, aproveitando ao máximo os recursos computacionais disponíveis e acelerando o processo de ajuste do modelo.

Assim como no gradiente boosting, o XGBoost também requer o ajuste adequado de hiperparâmetros para obter os melhores resultados. Isso inclui o número de árvores, a taxa de aprendizagem, a profundidade máxima da árvore e a força da regularização, entre outros.

O XGBoost ganhou popularidade na comunidade de ciência de dados e competições de machine learning devido à sua eficiência, precisão e flexibilidade. Ele foi usado com sucesso em muitos problemas do mundo real e demonstrou um desempenho impressionante em diversas tarefas de modelagem.

6.7 Vamos praticar

Primeiro, sempre, carregar os pacotes necessários para manipulação da base de dados e a base já tratada.

# Carregar pacotes e base de treino
library(tidyverse)
library(rpart)
base_treino = readRDS(file="salvos//base_treino_final.rds")

Para criar modelos de Gradiente Boosting será usado o pacote gbm (Chen et al. 2023).

#install.packages("xgboost")
library(xgboost)

Assim como para a Floresta Aleatória, para o Gradiente Boosting é fundamental fixar a semente para garantir a reprodutibilidade do código.

set.seed(123456789)

Serão replicados os mesmos exemplos feitos para os métodos já apresentados.

Regressão

Primeiro será ajustado um modelo para prever a nota em matemática das escolas. A função a ser usada é a xgboost, do pacote de mesmo nome. Um passo importante que precisa ser feito ao usar esta função é a transformação da base de dados, que é um data.frame, em matriz. A função xgboost não aceita data.frame como base de dados. E esta matriz deve conter somente as covariáveis.

X = base_treino |> select(SG_UF_ESCOLA,
                          TP_DEPENDENCIA_ADM_ESCOLA,
                          TP_LOCALIZACAO_ESCOLA,
                          NU_MATRICULAS,
                          INSE,
                          PC_FORMACAO_DOCENTE,
                          NU_TAXA_PERMANENCIA,
                          NU_TAXA_REPROVACAO,
                          NU_TAXA_ABANDONO,
                          PORTE_ESCOLA)
M_X = model.matrix(~. , data = X)[,-1]

É preciso informar o objetivo do método, que neste exemplo é realizar uma regressão. Por isso objective = "reg:squarederror". Neste momento também é possível indicamos valores para os hiperparâmetros aprendidos na aula de hoje: nrounds, número de árvores; subsample, proporção da base referente à subamostra; e eta, a taxa de aprendizagem.

XGB_REG <- xgboost(data = M_X,
                   label = base_treino$NU_MEDIA_MT,
                   objective = "reg:squarederror",
                   nrounds = 100,
                   subsample = 0.5,
                   eta = 0.1)

As variáveis importantes para esse modelo podem ser encontradas apartir do comando a seguir.

xgb.importance(model = XGB_REG)

                               Feature         Gain        Cover    Frequency
 1:  TP_DEPENDENCIA_ADM_ESCOLAEstadual 5.306025e-01 0.0470237078 0.0268548020
 2:                        INSEGrupo 6 1.421266e-01 0.0515623861 0.0277651343
 3:                        INSEGrupo 5 5.808020e-02 0.0545418463 0.0234410560
 4:                PC_FORMACAO_DOCENTE 4.484858e-02 0.1099405602 0.1522530724
 5:                NU_TAXA_PERMANENCIA 4.467215e-02 0.1664474935 0.1470186618
 6:                      NU_MATRICULAS 3.796238e-02 0.1003087951 0.1731907146
 7:                 NU_TAXA_REPROVACAO 2.533055e-02 0.0740887078 0.1206190259
 8:                   NU_TAXA_ABANDONO 2.295272e-02 0.0537934695 0.0698680018
 9:                     SG_UF_ESCOLAMG 1.869827e-02 0.0433338275 0.0229858898
10:                        INSEGrupo 4 1.310196e-02 0.0306511715 0.0193445608
11:                     SG_UF_ESCOLACE 6.500493e-03 0.0152983884 0.0129722349
12:                        INSEGrupo 3 6.390287e-03 0.0127827782 0.0147928994
13:                     SG_UF_ESCOLASP 4.789554e-03 0.0119504182 0.0152480655
14:                     SG_UF_ESCOLAPI 4.697503e-03 0.0086840403 0.0095584888
15: TP_DEPENDENCIA_ADM_ESCOLAMunicipal 3.918462e-03 0.0181334932 0.0097860719
16:                     SG_UF_ESCOLARJ 3.888793e-03 0.0164320119 0.0131998179
17:                     SG_UF_ESCOLABA 3.406202e-03 0.0108831444 0.0100136550
18:                     SG_UF_ESCOLAES 3.054521e-03 0.0271340395 0.0081929904
19:   TP_DEPENDENCIA_ADM_ESCOLAPrivada 2.643080e-03 0.0031961429 0.0088757396
20:                     SG_UF_ESCOLAPR 2.291903e-03 0.0069048521 0.0084205735
21:                        INSEGrupo 2 1.949605e-03 0.0029211801 0.0077378243
22:                     SG_UF_ESCOLADF 1.681868e-03 0.0168931722 0.0070550751
23:                     SG_UF_ESCOLARS 1.632417e-03 0.0045557140 0.0079654074
24:                     SG_UF_ESCOLASC 1.357340e-03 0.0030162216 0.0065999090
25:         TP_LOCALIZACAO_ESCOLARural 1.299975e-03 0.0049322934 0.0081929904
26:      PORTE_ESCOLADe 31 a 60 alunos 1.291697e-03 0.0041641910 0.0086481566
27:                     SG_UF_ESCOLAAM 1.278091e-03 0.0163716396 0.0065999090
28:                     SG_UF_ESCOLAGO 1.176924e-03 0.0046184773 0.0043240783
29:      PORTE_ESCOLADe 61 a 90 alunos 9.537991e-04 0.0021799763 0.0061447428
30:                     SG_UF_ESCOLATO 9.390284e-04 0.0056110329 0.0036413291
31:                     SG_UF_ESCOLAMA 8.921156e-04 0.0094025299 0.0045516614
32:                     SG_UF_ESCOLAAP 8.443140e-04 0.0117994876 0.0043240783
33:                     SG_UF_ESCOLAMS 8.218697e-04 0.0028076086 0.0034137460
34:                     SG_UF_ESCOLAPE 7.164451e-04 0.0034576563 0.0038689122
35:                     SG_UF_ESCOLARN 6.734673e-04 0.0030556728 0.0027309968
36:                     SG_UF_ESCOLARR 5.714803e-04 0.0120517360 0.0029585799
37:                     SG_UF_ESCOLAAL 5.164073e-04 0.0083349572 0.0034137460
38:                     SG_UF_ESCOLASE 4.795917e-04 0.0048967276 0.0031861629
39:                     SG_UF_ESCOLAMT 3.986054e-04 0.0059669901 0.0029585799
40:                     SG_UF_ESCOLAPB 3.413844e-04 0.0083762016 0.0038689122
41:                     SG_UF_ESCOLAPA 1.928292e-04 0.0001900829 0.0027309968
42:                     SG_UF_ESCOLARO 3.401746e-05 0.0013051764 0.0006827492
                               Feature         Gain        Cover    Frequency

A tabela apresentada mostra as variáveis ordenadas de acordo com sua importância no modelo, geralmente medido com base na redução média de ganho (Gain) ou na frequência em que a variável é selecionada para splits nas árvores do modelo (Frequency).

Já a coluna Cover representa a cobertura das variáveis, que representa a proporção de instâncias (observações) que são atribuídas a uma determinada ramificação do split. Quanto maior a cobertura média, maior a importância atribuída à variável, pois ela tem um impacto mais amplo na divisão dos dados e afeta uma proporção maior das instâncias de treinamento.

A função predict realiza a previsão também para o Gradiente Boosting, mas para o XGBoost é preciso informar o argumento newdata. Se queremos a previsão para os valores de treino, newdata será a matriz de covariáveis usadas para treinamento.

y_ = predict(XGB_REG,newdata = M_X)

A previsão pode ser feita pela mesma função predict.

y = base_treino$NU_MEDIA_MT
(RSS = sum((y - y_)^2))

[1] 9783911

(EMQ = mean((y-y_)^2))

[1] 836.2317

(R2 = 1 - sum((y-y_)^2)/sum((y-mean(y))^2))

[1] 0.8227031

Classificação Binária

Vamos repetir o processo de criar a nova variável resposta categória binária seguindo os critérios já estipulados. A questão principal aqui é que a função xgboost quando usada para problemas de classificação não recebe como label um objeto do tipo factor, o objeto passado como entrada no label precisa ser um vetor de números inteiros, começando em 0, que indica para cada observação qual a sua classe. Vamos usar 0 para a classe de interesse, “baixa” e 1 para a classe as outras classes.

TAXA_PART_BAIXA = ifelse(base_treino$TAXA_PART_CAT == "baixa",1,0)

A diferença na chamada da função xgboost para o caso de classificação é que agora objective = "binary:logistic", isso para o caso de classificação binária.

XGB_CLASS_2 <- xgboost(data = M_X,
                       label = TAXA_PART_BAIXA,
                       objective = "binary:logistic",
                       nrounds = 100,
                       subsample = 0.5,
                       eta = 0.1)

xgb.importance(model = XGB_CLASS_2)

                               Feature         Gain       Cover    Frequency
 1:  TP_DEPENDENCIA_ADM_ESCOLAEstadual 0.3322269015 0.055190929 0.0111492281
 2:                   NU_TAXA_ABANDONO 0.1018848439 0.127020347 0.1203544883
 3:                      NU_MATRICULAS 0.0885588885 0.133749796 0.1523727844
 4:                PC_FORMACAO_DOCENTE 0.0861221876 0.107803145 0.1723842196
 5:                NU_TAXA_PERMANENCIA 0.0787436100 0.086133794 0.1558033162
 6:                 NU_TAXA_REPROVACAO 0.0706085049 0.074390866 0.1532304174
 7:                     SG_UF_ESCOLACE 0.0417988890 0.045702664 0.0131503716
 8:                     SG_UF_ESCOLAES 0.0306106392 0.039266300 0.0117209834
 9:                     SG_UF_ESCOLASP 0.0300227300 0.048693018 0.0288736421
10:   TP_DEPENDENCIA_ADM_ESCOLAPrivada 0.0125306420 0.012270462 0.0051457976
11:                     SG_UF_ESCOLAPR 0.0115561333 0.025864864 0.0114351058
12:                        INSEGrupo 3 0.0109025980 0.009900962 0.0162950257
13:                     SG_UF_ESCOLARJ 0.0101351635 0.020070681 0.0137221269
14:                     SG_UF_ESCOLARS 0.0096587244 0.008695351 0.0094339623
15:                        INSEGrupo 5 0.0090480287 0.014128085 0.0100057176
16:                     SG_UF_ESCOLADF 0.0077094329 0.016044545 0.0042881647
17:                        INSEGrupo 4 0.0071768929 0.010361157 0.0137221269
18:                        INSEGrupo 6 0.0058435602 0.020503478 0.0062893082
19:                     SG_UF_ESCOLASC 0.0053969417 0.015859602 0.0077186964
20:                     SG_UF_ESCOLAMG 0.0052533039 0.010009167 0.0062893082
21:                     SG_UF_ESCOLAPB 0.0051240884 0.013155829 0.0057175529
22:         TP_LOCALIZACAO_ESCOLARural 0.0047004174 0.008553865 0.0082904517
23:                     SG_UF_ESCOLAPE 0.0037880269 0.006780661 0.0060034305
24:      PORTE_ESCOLADe 61 a 90 alunos 0.0036696142 0.003004429 0.0091480846
25:      PORTE_ESCOLADe 31 a 60 alunos 0.0035405178 0.003540034 0.0077186964
26:                     SG_UF_ESCOLARO 0.0031767054 0.014203266 0.0040022870
27:                     SG_UF_ESCOLAMS 0.0029189961 0.010840577 0.0037164094
28:                     SG_UF_ESCOLAMT 0.0025245631 0.007909155 0.0040022870
29: TP_DEPENDENCIA_ADM_ESCOLAMunicipal 0.0023223987 0.005414093 0.0042881647
30:                        INSEGrupo 2 0.0018766826 0.002256625 0.0054316752
31:                     SG_UF_ESCOLAAL 0.0012792843 0.005546506 0.0017152659
32:                     SG_UF_ESCOLAAP 0.0011583039 0.004559350 0.0014293882
33:                     SG_UF_ESCOLASE 0.0011578520 0.004610113 0.0014293882
34:                     SG_UF_ESCOLARN 0.0011502140 0.004746855 0.0020011435
35:                     SG_UF_ESCOLAGO 0.0010717238 0.004824626 0.0017152659
36:                     SG_UF_ESCOLABA 0.0009279159 0.001116255 0.0020011435
37:                     SG_UF_ESCOLATO 0.0008861752 0.001334537 0.0011435106
38:                     SG_UF_ESCOLAAM 0.0008066465 0.004097937 0.0022870212
39:                     SG_UF_ESCOLAMA 0.0007185597 0.003081973 0.0011435106
40:                     SG_UF_ESCOLAPI 0.0006590842 0.003366700 0.0011435106
41:                     SG_UF_ESCOLARR 0.0004864148 0.004123949 0.0014293882
42:                     SG_UF_ESCOLAPA 0.0002671990 0.001273455 0.0008576329
                               Feature         Gain       Cover    Frequency

y_= predict(XGB_CLASS_2, newdata = M_X)
head(y_)

[1] 0.007230997 0.013061869 0.146902934 0.118033834 0.017095475 0.666431665

Para gerar a curva ROC, o pacote pROC (Robin et al. 2011) .

library(pROC)
ROC = roc(response = TAXA_PART_BAIXA,predictor = y_)
plot.roc(ROC,
         print.auc = TRUE,
         print.thres = TRUE)

y_classe = ifelse(y_>0.402,1,0)
library(caret)
confusionMatrix(as.factor(TAXA_PART_BAIXA),as.factor(y_classe))

Confusion Matrix and Statistics

          Reference
Prediction    0    1
         0 6403 1334
         1  420 3543
                                          
               Accuracy : 0.8501          
                 95% CI : (0.8435, 0.8565)
    No Information Rate : 0.5832          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.6832          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       
                                          
            Sensitivity : 0.9384          
            Specificity : 0.7265          
         Pos Pred Value : 0.8276          
         Neg Pred Value : 0.8940          
             Prevalence : 0.5832          
         Detection Rate : 0.5473          
   Detection Prevalence : 0.6613          
      Balanced Accuracy : 0.8325          
                                          
       'Positive' Class : 0

Classificação Multiclasses

Vejamos agora o desempenho do método de XGBoost para o problema de classificação com 3 classes. Para o XGBoost é preciso definir a variável resposta como um vetor de números inteiros, começando em 0.

Y = ifelse(base_treino$TAXA_PART_CAT == "baixa",0,ifelse(base_treino$TAXA_PART_CAT =="media",1,2))

Dessa vez mais duas mudanças serão feitas na chamada da função xgboost. Agora objective = "multi:softprob", para indicar que o problema é multiclasse, e ainda é preciso informar o número de classes com num_class = 3.

XGB_CLASS_3 <- xgboost(data = M_X,
                       label = Y,
                       num_class = 3,
                       objective = "multi:softprob",
                       nrounds = 100,
                       subsample = 0.5,
                       eta = 0.1)

xgb.importance(model = XGB_CLASS_3)

                               Feature         Gain       Cover    Frequency
 1:  TP_DEPENDENCIA_ADM_ESCOLAEstadual 0.2727811654 0.034564888 0.0133689840
 2:                   NU_TAXA_ABANDONO 0.1199948931 0.116569799 0.1121323529
 3:                      NU_MATRICULAS 0.1000411470 0.153859671 0.1642713904
 4:                PC_FORMACAO_DOCENTE 0.0961483362 0.116658502 0.1724598930
 5:                NU_TAXA_PERMANENCIA 0.0936839499 0.116600599 0.1650233957
 6:                 NU_TAXA_REPROVACAO 0.0803653654 0.085124732 0.1479779412
 7:                     SG_UF_ESCOLACE 0.0320501296 0.032071725 0.0134525401
 8:                     SG_UF_ESCOLASP 0.0280441310 0.039020730 0.0205548128
 9:                     SG_UF_ESCOLAES 0.0262090168 0.028509726 0.0113636364
10:   TP_DEPENDENCIA_ADM_ESCOLAPrivada 0.0129114855 0.011996542 0.0063502674
11:                     SG_UF_ESCOLARJ 0.0128809306 0.016292892 0.0122827540
12:                     SG_UF_ESCOLAPR 0.0124792929 0.023698776 0.0103609626
13:                        INSEGrupo 5 0.0107345898 0.012328820 0.0127840909
14:                        INSEGrupo 3 0.0097443905 0.009796788 0.0127840909
15:                        INSEGrupo 4 0.0093251556 0.007584515 0.0122827540
16:                        INSEGrupo 6 0.0090997452 0.016903697 0.0103609626
17:                     SG_UF_ESCOLARS 0.0081488650 0.018073619 0.0085227273
18:                     SG_UF_ESCOLASC 0.0061832352 0.014451679 0.0071858289
19:                     SG_UF_ESCOLAMG 0.0060812322 0.013920093 0.0065173797
20:                     SG_UF_ESCOLADF 0.0054708933 0.015582243 0.0041778075
21:                     SG_UF_ESCOLAPB 0.0047707776 0.011277866 0.0055147059
22:                        INSEGrupo 2 0.0041598836 0.006451424 0.0083556150
23:         TP_LOCALIZACAO_ESCOLARural 0.0039590747 0.004112651 0.0069351604
24:      PORTE_ESCOLADe 31 a 60 alunos 0.0034448331 0.002215143 0.0069351604
25:                     SG_UF_ESCOLAPE 0.0032061872 0.004129742 0.0045955882
26:                     SG_UF_ESCOLARO 0.0030046108 0.011809205 0.0040942513
27:      PORTE_ESCOLADe 61 a 90 alunos 0.0028705639 0.001548225 0.0070187166
28:                     SG_UF_ESCOLABA 0.0025806831 0.010966552 0.0037600267
29: TP_DEPENDENCIA_ADM_ESCOLAMunicipal 0.0025342391 0.004240667 0.0033422460
30:                     SG_UF_ESCOLAMS 0.0023464265 0.007276857 0.0025902406
31:                     SG_UF_ESCOLAPI 0.0019621460 0.004616369 0.0030915775
32:                     SG_UF_ESCOLAGO 0.0017955115 0.005018477 0.0030080214
33:                     SG_UF_ESCOLAPA 0.0015833750 0.005735725 0.0020053476
34:                     SG_UF_ESCOLAMT 0.0014595957 0.005411581 0.0024231283
35:                     SG_UF_ESCOLATO 0.0012910209 0.005829560 0.0019217914
36:                     SG_UF_ESCOLASE 0.0012854201 0.004845362 0.0017546791
37:                     SG_UF_ESCOLARN 0.0012777760 0.003827110 0.0020053476
38:                     SG_UF_ESCOLAAM 0.0010629903 0.002148442 0.0016711230
39:                     SG_UF_ESCOLAAL 0.0009061358 0.005312866 0.0015875668
40:                     SG_UF_ESCOLAMA 0.0008524803 0.002445415 0.0013368984
41:                     SG_UF_ESCOLAAP 0.0007917829 0.004139428 0.0009191176
42:                     SG_UF_ESCOLARR 0.0004765355 0.003031297 0.0009191176
                               Feature         Gain       Cover    Frequency

Para realizar a previsão com a função predict, lembrando que em um objeto da class “xgb.Booster” é preciso informar o argumento newdata.

predict(XGB_CLASS_3,newdata=M_X)

    [1] 0.005048582 0.120415643 0.874535799 0.018599473 0.343623400 0.637777150
    [7] 0.140126988 0.298844337 0.561028659 0.215170622 0.553240538 0.231588826
   [13] 0.032674577 0.371185720 0.596139729 0.721569836 0.262757033 0.015673090
   [19] 0.375060320 0.250211477 0.374728233 0.388041288 0.553800166 0.058158521
   [25] 0.320265979 0.665694296 0.014039733 0.197767615 0.719515383 0.082716979
   [31] 0.021728016 0.145924851 0.832347095 0.802626371 0.154699773 0.042673837
   [37] 0.699973345 0.274620771 0.025405882 0.313374877 0.345659316 0.340965778
   [43] 0.321086347 0.319072366 0.359841287 0.734190345 0.239601716 0.026207903
   [49] 0.911634862 0.078250386 0.010114753 0.662990510 0.301211685 0.035797834
   [55] 0.355923951 0.278810591 0.365265429 0.248273090 0.404241353 0.347485512
   [61] 0.327105284 0.627952456 0.044942267 0.769827724 0.208441064 0.021731181
   [67] 0.794421554 0.180789858 0.024788555 0.167649403 0.570021451 0.262329161
   [73] 0.332307607 0.624118030 0.043574385 0.023168048 0.161093011 0.815738916
   [79] 0.832803249 0.149446636 0.017750086 0.568659484 0.386870623 0.044469889
   [85] 0.347372919 0.533573210 0.119053863 0.270322412 0.475254178 0.254423410
   [91] 0.862651408 0.125325024 0.012023501 0.748043180 0.239529178 0.012427661
   [97] 0.291402549 0.509013772 0.199583679 0.004128671 0.148118481 0.847752869
  [103] 0.484937727 0.426000237 0.089062072 0.743378103 0.231093943 0.025527943
  [109] 0.569291472 0.368311018 0.062397480 0.489817679 0.412629873 0.097552419
  [115] 0.006538462 0.030589182 0.962872386 0.639962852 0.331126988 0.028910158
  [121] 0.646180928 0.316683501 0.037135564 0.016607089 0.428875625 0.554517329
  [127] 0.807471395 0.155606598 0.036922034 0.438383043 0.543733776 0.017883129
  [133] 0.618114233 0.325802535 0.056083225 0.382960558 0.572057128 0.044982273
  [139] 0.753856361 0.225958079 0.020185547 0.720805407 0.241498172 0.037696406
  [145] 0.015131713 0.384917080 0.599951208 0.043187801 0.336710930 0.620101273
  [151] 0.535952210 0.431373328 0.032674484 0.774423301 0.210520133 0.015056553
  [157] 0.280310422 0.675244331 0.044445295 0.711810410 0.265240788 0.022948777
  [163] 0.448237360 0.419493228 0.132269457 0.143654421 0.596844494 0.259501040
  [169] 0.541225433 0.430244744 0.028529771 0.579648912 0.394560456 0.025790649
  [175] 0.005349430 0.246938258 0.747712255 0.358727932 0.461943328 0.179328769
  [181] 0.622036994 0.350659460 0.027303532 0.757287502 0.218673736 0.024038712
  [187] 0.572234869 0.399734914 0.028030232 0.242614478 0.715465367 0.041920140
  [193] 0.161807388 0.751230657 0.086962007 0.373218119 0.560712516 0.066069372
  [199] 0.329180330 0.533602417 0.137217268 0.220009580 0.610086620 0.169903845
  [205] 0.854251266 0.125635952 0.020112839 0.931945443 0.058504932 0.009549570
  [211] 0.259849668 0.463352829 0.276797473 0.551916659 0.210204616 0.237878680
  [217] 0.824051440 0.149307683 0.026640860 0.419182450 0.535733938 0.045083642
  [223] 0.818775892 0.164357111 0.016866937 0.056341778 0.277714103 0.665944159
  [229] 0.832213819 0.155576304 0.012209883 0.029741233 0.278806269 0.691452444
  [235] 0.095005669 0.160155728 0.744838655 0.488700479 0.262884796 0.248414695
  [241] 0.389343262 0.592207968 0.018448779 0.207489267 0.598897815 0.193612933
  [247] 0.734648764 0.247296527 0.018054776 0.666169524 0.319824308 0.014006120
  [253] 0.471006364 0.455032080 0.073961601 0.309552968 0.497767508 0.192679524
  [259] 0.507426262 0.455436796 0.037136916 0.380156606 0.413549721 0.206293732
  [265] 0.638087153 0.335497856 0.026414948 0.303062141 0.292437255 0.404500574
  [271] 0.267522961 0.351613939 0.380863070 0.443945408 0.430817306 0.125237301
  [277] 0.799869120 0.183662429 0.016468491 0.022679286 0.179081172 0.798239529
  [283] 0.032980628 0.915383697 0.051635716 0.724490345 0.255827188 0.019682413
  [289] 0.018990336 0.164852440 0.816157281 0.773329437 0.203311428 0.023359157
  [295] 0.447030187 0.444364190 0.108605638 0.857139468 0.124715365 0.018145131
  [301] 0.359671921 0.498355806 0.141972303 0.410920978 0.551161051 0.037917972
  [307] 0.704941392 0.269702822 0.025355740 0.023586618 0.150614455 0.825798869
  [313] 0.014954914 0.465854168 0.519190907 0.818586051 0.170792446 0.010621478
  [319] 0.026588153 0.288021833 0.685389996 0.007872860 0.515076458 0.477050662
  [325] 0.420639992 0.325103104 0.254256845 0.022333356 0.455977023 0.521689653
  [331] 0.014739284 0.189358816 0.795901895 0.035354391 0.310037673 0.654607952
  [337] 0.547886550 0.429327101 0.022786360 0.411636174 0.497165322 0.091198526
  [343] 0.890082777 0.099482916 0.010434324 0.213874772 0.532996356 0.253128827
  [349] 0.109898932 0.638070166 0.252030849 0.010487719 0.047701310 0.941811025
  [355] 0.396000564 0.568795025 0.035204414 0.032674327 0.126442343 0.840883315
  [361] 0.762464046 0.187443107 0.050092902 0.035424247 0.328027129 0.636548579
  [367] 0.058012992 0.341710180 0.600276887 0.053749029 0.386659890 0.559591115
  [373] 0.071095616 0.360996783 0.567907572 0.333661556 0.342693627 0.323644847
  [379] 0.705722988 0.261391640 0.032885335 0.860211074 0.132869393 0.006919519
  [385] 0.669799984 0.298089325 0.032110654 0.737307310 0.225644752 0.037047949
  [391] 0.527289927 0.437921256 0.034788806 0.779195547 0.208949089 0.011855404
  [397] 0.702336013 0.287977844 0.009686110 0.018051723 0.161907524 0.820040762
  [403] 0.010864941 0.183822095 0.805312991 0.629828691 0.345112801 0.025058547
  [409] 0.812625051 0.178369597 0.009005376 0.649366438 0.330176890 0.020456696
  [415] 0.305189133 0.483436853 0.211374030 0.736417353 0.246920452 0.016662247
  [421] 0.662550032 0.313912302 0.023537660 0.657930434 0.319125801 0.022943767
  [427] 0.108126730 0.224387288 0.667485952 0.735857010 0.252052844 0.012090165
  [433] 0.434836656 0.392583996 0.172579378 0.520707369 0.436954051 0.042338539
  [439] 0.570548117 0.391504109 0.037947770 0.788673341 0.197788402 0.013538277
  [445] 0.036753997 0.291252911 0.671993077 0.640234649 0.330624461 0.029140899
  [451] 0.584413946 0.371556580 0.044029482 0.034293793 0.240887865 0.724818349
  [457] 0.017189700 0.216243252 0.766566992 0.020286454 0.135344893 0.844368637
  [463] 0.724228263 0.252475530 0.023296194 0.621499658 0.325891942 0.052608389
  [469] 0.534556448 0.437993139 0.027450452 0.008089072 0.172724649 0.819186211
  [475] 0.741913795 0.219138980 0.038947236 0.085618563 0.231850430 0.682530999
  [481] 0.039232917 0.063177079 0.897590041 0.628475070 0.351195306 0.020329630
  [487] 0.768564224 0.221767142 0.009668593 0.745780945 0.243583903 0.010635164
  [493] 0.754072845 0.164537951 0.081389181 0.663173139 0.312321097 0.024505772
  [499] 0.748645186 0.218931496 0.032423347 0.701604187 0.249722883 0.048672877
  [505] 0.350999117 0.290035993 0.358964920 0.615867019 0.301779240 0.082353748
  [511] 0.320568383 0.400038987 0.279392600 0.846631587 0.131062835 0.022305578
  [517] 0.512308836 0.431617379 0.056073777 0.805973470 0.187954068 0.006072477
  [523] 0.821450889 0.164832100 0.013717031 0.835181236 0.150528595 0.014290160
  [529] 0.846693814 0.135091454 0.018214740 0.764062464 0.219565272 0.016372293
  [535] 0.041831795 0.196792901 0.761375308 0.027387924 0.349306852 0.623305261
  [541] 0.065615878 0.437835485 0.496548682 0.034880709 0.200775817 0.764343500
  [547] 0.012946476 0.063971706 0.923081875 0.041515637 0.268148363 0.690336049
  [553] 0.052696895 0.279059947 0.668243170 0.093669713 0.356168896 0.550161362
  [559] 0.072241679 0.347561270 0.580197036 0.026825905 0.058489263 0.914684772
  [565] 0.023759278 0.262429714 0.713810980 0.351480991 0.385732293 0.262786746
  [571] 0.029091990 0.202640980 0.768267035 0.040961191 0.211983725 0.747055113
  [577] 0.025246289 0.175428927 0.799324751 0.195646599 0.336914122 0.467439324
  [583] 0.026270697 0.161518872 0.812210441 0.020423580 0.186556548 0.793019891
  [589] 0.243974999 0.336591035 0.419433922 0.031260651 0.160205632 0.808533669
  [595] 0.675448477 0.296964645 0.027586903 0.606008828 0.349457264 0.044533879
  [601] 0.791327119 0.198836133 0.009836792 0.605835378 0.353854686 0.040309966
  [607] 0.801686585 0.189011768 0.009301683 0.534209907 0.370602995 0.095187098
  [613] 0.698022068 0.285290778 0.016687173 0.763805032 0.211356252 0.024838667
  [619] 0.417333007 0.537126124 0.045540858 0.550870061 0.415707290 0.033422634
  [625] 0.123803928 0.183126330 0.693069696 0.443794608 0.463946581 0.092258848
  [631] 0.416240454 0.339234322 0.244525254 0.051927824 0.312543213 0.635528982
  [637] 0.813450933 0.171704918 0.014844151 0.168225423 0.272870839 0.558903754
  [643] 0.369850248 0.532238901 0.097910874 0.315956593 0.603764176 0.080279171
  [649] 0.789114118 0.200358033 0.010527884 0.873065114 0.114749305 0.012185531
  [655] 0.644691467 0.315912545 0.039396018 0.616314292 0.331068993 0.052616753
  [661] 0.722946346 0.247290552 0.029763136 0.470794320 0.481067628 0.048138060
  [667] 0.200648069 0.400790721 0.398561209 0.058753144 0.260805100 0.680441737
  [673] 0.044510696 0.239031598 0.716457725 0.076385014 0.188759059 0.734855890
  [679] 0.162023723 0.308159798 0.529816508 0.022933336 0.092197061 0.884869576
  [685] 0.033943411 0.209109530 0.756947041 0.033546839 0.450668752 0.515784383
  [691] 0.821339965 0.159895390 0.018764626 0.273658752 0.327841818 0.398499459
  [697] 0.757301450 0.215867415 0.026831146 0.764406025 0.225642040 0.009951951
  [703] 0.779841959 0.203218013 0.016940065 0.360508531 0.287587345 0.351904124
  [709] 0.825953066 0.165856034 0.008190902 0.260724664 0.437056959 0.302218348
  [715] 0.605524421 0.351189345 0.043286212 0.042655185 0.480620623 0.476724148
  [721] 0.647900760 0.229610309 0.122488908 0.555341244 0.430204362 0.014454396
  [727] 0.018584123 0.109496199 0.871919632 0.911412120 0.079855740 0.008732117
  [733] 0.515370786 0.441528022 0.043101192 0.667679310 0.312588692 0.019731989
  [739] 0.899205029 0.094181649 0.006613302 0.788108826 0.203279465 0.008611700
  [745] 0.030737637 0.134391412 0.834870934 0.806281805 0.176880300 0.016837930
  [751] 0.185030699 0.323823869 0.491145492 0.212628707 0.678393841 0.108977422
  [757] 0.635855556 0.307814807 0.056329701 0.834717274 0.150001779 0.015280982
  [763] 0.797009587 0.191534773 0.011455597 0.686912894 0.280124396 0.032962691
  [769] 0.132025912 0.253923327 0.614050746 0.751893699 0.238033175 0.010073099
  [775] 0.150771260 0.772864163 0.076364584 0.048210267 0.196541250 0.755248547
  [781] 0.783646464 0.206800058 0.009553434 0.501498997 0.475007266 0.023493739
  [787] 0.179978833 0.680840671 0.139180511 0.091312245 0.286642283 0.622045457
  [793] 0.651518464 0.326957941 0.021523530 0.867118895 0.116162561 0.016718553
  [799] 0.125439703 0.209767118 0.664793134 0.071102999 0.274637699 0.654259324
  [805] 0.051075999 0.260873348 0.688050628 0.830099940 0.156911105 0.012988935
  [811] 0.044076324 0.286357343 0.669566333 0.080426738 0.177309066 0.742264152
  [817] 0.094208553 0.202426076 0.703365326 0.014509827 0.130972385 0.854517758
  [823] 0.091556847 0.194401458 0.714041650 0.081345119 0.302428395 0.616226494
  [829] 0.027637472 0.107687280 0.864675224 0.863329709 0.127899647 0.008770590
  [835] 0.223677188 0.380725801 0.395596951 0.102054916 0.237995863 0.659949243
  [841] 0.323751032 0.302132249 0.374116719 0.855373085 0.133632004 0.010994924
  [847] 0.636602759 0.314356506 0.049040727 0.318989277 0.465497464 0.215513259
  [853] 0.094322421 0.238647535 0.667029977 0.643043041 0.322695792 0.034261115
  [859] 0.195317611 0.228213772 0.576468647 0.424793214 0.446972668 0.128234163
  [865] 0.484252602 0.482960850 0.032786597 0.479277223 0.474862546 0.045860227
  [871] 0.533483922 0.357634604 0.108881451 0.631468296 0.331028730 0.037502956
  [877] 0.837194383 0.149889901 0.012915766 0.090555944 0.246979088 0.662464976
  [883] 0.832509160 0.156289801 0.011201053 0.038443521 0.297773629 0.663782835
  [889] 0.057079960 0.209687576 0.733232498 0.682598472 0.288404405 0.028997155
  [895] 0.033310700 0.147534385 0.819154859 0.813224137 0.175380096 0.011395742
  [901] 0.402423382 0.437674880 0.159901768 0.805357575 0.186165735 0.008476648
  [907] 0.818674207 0.172341093 0.008984699 0.489379227 0.419859082 0.090761706
  [913] 0.377050936 0.588967443 0.033981632 0.809668541 0.182089090 0.008242358
  [919] 0.868773162 0.122883514 0.008343253 0.741966724 0.240315661 0.017717624
  [925] 0.847396135 0.141743794 0.010860099 0.052383579 0.214666128 0.732950270
  [931] 0.151345715 0.407699704 0.440954536 0.019874493 0.217627466 0.762498081
  [937] 0.840492845 0.147763610 0.011743490 0.814277887 0.172171518 0.013550573
  [943] 0.700438857 0.285324246 0.014236872 0.052651037 0.117272779 0.830076158
  [949] 0.022265702 0.176219210 0.801515102 0.756630719 0.210243911 0.033125348
  [955] 0.018993240 0.177276880 0.803729951 0.871574044 0.113709345 0.014716659
  [961] 0.038348734 0.293610692 0.668040633 0.014230589 0.078492649 0.907276750
  [967] 0.014708574 0.115580708 0.869710743 0.289739907 0.271812409 0.438447714
  [973] 0.246554986 0.234964550 0.518480480 0.563270748 0.385904849 0.050824370
  [979] 0.620537579 0.367676824 0.011785623 0.862531483 0.127676025 0.009792445
  [985] 0.811682343 0.178554431 0.009763218 0.869715452 0.121331558 0.008952977
  [991] 0.763379574 0.218763903 0.017856522 0.784512877 0.202303946 0.013183189
  [997] 0.298076451 0.256013244 0.445910305 0.032661241 0.198907077 0.768431664
 [1003] 0.816064298 0.165899724 0.018035984 0.845762670 0.139979348 0.014258035
 [1009] 0.867853999 0.123394951 0.008751070 0.819301665 0.168854222 0.011844119
 [1015] 0.851309299 0.140664250 0.008026406 0.373844326 0.465277493 0.160878152
 [1021] 0.716000259 0.272635430 0.011364310 0.815618992 0.174773321 0.009607636
 [1027] 0.789198875 0.197254464 0.013546646 0.647987008 0.343300045 0.008712959
 [1033] 0.547347248 0.432524770 0.020127941 0.831281900 0.160793886 0.007924144
 [1039] 0.907625496 0.081519850 0.010854601 0.587705374 0.382056028 0.030238634
 [1045] 0.810457826 0.183184713 0.006357484 0.871761501 0.116245620 0.011992844
 [1051] 0.552204609 0.421451956 0.026343435 0.535765648 0.454899549 0.009334837
 [1057] 0.796281159 0.195181698 0.008537148 0.842383325 0.147908077 0.009708595
 [1063] 0.019797556 0.130957946 0.849244535 0.020693621 0.133513346 0.845793068
 [1069] 0.026123656 0.206217900 0.767658472 0.299299687 0.654256284 0.046444047
 [1075] 0.054365680 0.418344647 0.527289689 0.003291681 0.128694683 0.868013620
 [1081] 0.011361974 0.083411567 0.905226469 0.635538518 0.349791259 0.014670226
 [1087] 0.012896546 0.109465294 0.877638161 0.037288610 0.282455921 0.680255413
 [1093] 0.094521806 0.271676421 0.633801758 0.562907398 0.361684054 0.075408511
 [1099] 0.929604709 0.062853925 0.007541390 0.028653273 0.124361567 0.846985161
 [1105] 0.716597140 0.269074172 0.014328642 0.022102408 0.259671628 0.718225956
 [1111] 0.776498139 0.215197921 0.008303917 0.714615166 0.273964584 0.011420236
 [1117] 0.616274178 0.365857691 0.017868146 0.933181167 0.059404500 0.007414321
 [1123] 0.634544730 0.352332264 0.013123030 0.724315643 0.259187967 0.016496362
 [1129] 0.862995863 0.117156431 0.019847739 0.836706340 0.135046095 0.028247541
 [1135] 0.849107981 0.139273942 0.011618100 0.921579242 0.069546938 0.008873837
 [1141] 0.803402603 0.185527056 0.011070272 0.801363707 0.189064354 0.009571915
 [1147] 0.608545780 0.349802971 0.041651182 0.952171385 0.042111509 0.005717118
 [1153] 0.690843523 0.282018960 0.027137531 0.788656116 0.199867889 0.011476028
 [1159] 0.931774974 0.061963148 0.006261869 0.833610117 0.157698050 0.008691791
 [1165] 0.443488955 0.433026224 0.123484753 0.011090402 0.087692261 0.901217401
 [1171] 0.014380182 0.109144159 0.876475632 0.611607134 0.363889307 0.024503609
 [1177] 0.018371716 0.109811530 0.871816754 0.069544718 0.366316229 0.564139068
 [1183] 0.030837512 0.266591758 0.702570736 0.912082791 0.080295555 0.007621627
 [1189] 0.748001993 0.243447036 0.008551021 0.699446619 0.290797710 0.009755660
 [1195] 0.927489460 0.060479216 0.012031335 0.824511826 0.166859001 0.008629222
 [1201] 0.502415776 0.475564718 0.022019502 0.117357463 0.353882819 0.528759658
 [1207] 0.732239306 0.223909557 0.043851160 0.545194089 0.381171256 0.073634647
 [1213] 0.718231976 0.225988775 0.055779263 0.621194482 0.327709436 0.051096078
 [1219] 0.951848745 0.043898609 0.004252668 0.866105556 0.125368446 0.008526046
 [1225] 0.871824861 0.121645011 0.006530192 0.020192400 0.166491076 0.813316584
 [1231] 0.018620182 0.141159847 0.840219915 0.882102430 0.111348264 0.006549351
 [1237] 0.751009941 0.214123547 0.034866534 0.738446951 0.240137368 0.021415697
 [1243] 0.443139046 0.425753981 0.131106898 0.841507077 0.147479266 0.011013687
 [1249] 0.035178006 0.293862551 0.670959473 0.396146894 0.553395331 0.050457750
 [1255] 0.926638484 0.065182857 0.008178639 0.100211889 0.421661049 0.478127092
 [1261] 0.903519750 0.088595130 0.007885071 0.799506128 0.189222589 0.011271295
 [1267] 0.730558693 0.201068446 0.068372883 0.881758451 0.109460928 0.008780678
 [1273] 0.623057961 0.334019005 0.042923074 0.827444077 0.164643288 0.007912671
 [1279] 0.033449605 0.144593686 0.821956694 0.773703992 0.215491205 0.010804781
 [1285] 0.019237379 0.138630822 0.842131793 0.036197238 0.369533122 0.594269633
 [1291] 0.155555099 0.236999959 0.607444942 0.028329384 0.221368030 0.750302613
 [1297] 0.510083139 0.469763726 0.020153170 0.418827832 0.219647869 0.361524314
 [1303] 0.921157479 0.072381385 0.006461126 0.021091463 0.179905623 0.799002886
 [1309] 0.847386539 0.136249423 0.016364103 0.649369478 0.310933053 0.039697465
 [1315] 0.020730950 0.091781989 0.887487113 0.040707085 0.301486969 0.657805979
 [1321] 0.025042359 0.137377411 0.837580204 0.783626199 0.200668707 0.015705129
 [1327] 0.545195043 0.430031031 0.024773914 0.025117876 0.186571836 0.788310230
 [1333] 0.955206931 0.040003702 0.004789401 0.900068223 0.091188632 0.008743166
 [1339] 0.024211161 0.143616170 0.832172632 0.046680834 0.170768335 0.782550871
 [1345] 0.934423327 0.058202919 0.007373787 0.016671820 0.103696398 0.879631817
 [1351] 0.596284866 0.356812656 0.046902508 0.047923733 0.261487007 0.690589249
 [1357] 0.029944928 0.139402509 0.830652535 0.090293400 0.406920016 0.502786577
 [1363] 0.038307533 0.224911198 0.736781299 0.015301875 0.102486417 0.882211685
 [1369] 0.006263492 0.643201113 0.350535393 0.029708099 0.207932740 0.762359142
 [1375] 0.053836316 0.310490876 0.635672808 0.025023153 0.140824378 0.834152400
 [1381] 0.027311606 0.204279065 0.768409371 0.003376225 0.244561329 0.752062440
 [1387] 0.042338122 0.221833557 0.735828340 0.069455780 0.277597129 0.652947128
 [1393] 0.038304333 0.210983917 0.750711679 0.064005218 0.267702430 0.668292344
 [1399] 0.028435383 0.151596725 0.819967866 0.017311888 0.048154064 0.934534013
 [1405] 0.040362574 0.158089131 0.801548243 0.026357740 0.113186203 0.860456109
 [1411] 0.014963389 0.057359099 0.927677453 0.013038542 0.156086475 0.830875039
 [1417] 0.029642453 0.133897185 0.836460352 0.057241645 0.194033280 0.748725057
 [1423] 0.032565232 0.137233585 0.830201209 0.046387091 0.144950360 0.808662593
 [1429] 0.027476115 0.080091819 0.892432094 0.034476299 0.116041094 0.849482536
 [1435] 0.010762442 0.072596453 0.916641116 0.055791851 0.139985412 0.804222763
 [1441] 0.025411149 0.184207991 0.790380895 0.081151225 0.312568873 0.606279910
 [1447] 0.380123228 0.436577827 0.183298945 0.919365585 0.071891129 0.008743230
 [1453] 0.847988188 0.132150888 0.019860854 0.020006534 0.120182037 0.859811366
 [1459] 0.004023374 0.046842381 0.949134231 0.026054110 0.147010297 0.826935589
 [1465] 0.020455133 0.139439374 0.840105474 0.026032085 0.132194281 0.841773570
 [1471] 0.033775624 0.242383868 0.723840535 0.029726297 0.209163666 0.761110067
 [1477] 0.863144934 0.123966523 0.012888521 0.946711719 0.046974026 0.006314234
 [1483] 0.023819024 0.148659721 0.827521265 0.648791492 0.325482100 0.025726393
 [1489] 0.016786637 0.138410807 0.844802558 0.877711296 0.116605021 0.005683733
 [1495] 0.952268243 0.042177539 0.005554171 0.023334296 0.170605645 0.806060016
 [1501] 0.028916378 0.192373693 0.778709948 0.927329540 0.065656029 0.007014478
 [1507] 0.047045190 0.315292954 0.637661874 0.140902147 0.578748882 0.280348986
 [1513] 0.936870158 0.056423459 0.006706379 0.098499812 0.551741183 0.349759042
 [1519] 0.430237919 0.424216241 0.145545810 0.025358321 0.150788009 0.823853672
 [1525] 0.458087802 0.482299477 0.059612662 0.030057605 0.216204032 0.753738344
 [1531] 0.014266416 0.099614680 0.886118948 0.013448196 0.099538095 0.887013674
 [1537] 0.654877424 0.264690191 0.080432393 0.094474800 0.263978779 0.641546428
 [1543] 0.014695367 0.118784294 0.866520405 0.799689889 0.188636467 0.011673620
 [1549] 0.474794894 0.495333642 0.029871399 0.017108422 0.156554163 0.826337397
 [1555] 0.022269817 0.173128381 0.804601848 0.058611628 0.351922423 0.589465976
 [1561] 0.023292277 0.162802652 0.813905060 0.023613978 0.178525403 0.797860682
 [1567] 0.009285584 0.084708571 0.906005800 0.018984113 0.201700211 0.779315650
 [1573] 0.032972667 0.228986129 0.738041222 0.839183629 0.150145292 0.010671042
 [1579] 0.924499094 0.067102700 0.008398166 0.012358502 0.118048295 0.869593203
 [1585] 0.021345373 0.111329898 0.867324769 0.024046995 0.184394717 0.791558325
 [1591] 0.794855595 0.195299968 0.009844470 0.800108731 0.185500816 0.014390493
 [1597] 0.010064329 0.183538288 0.806397438 0.935787857 0.056802519 0.007409690
 [1603] 0.940683246 0.053115517 0.006201175 0.919832468 0.074364103 0.005803474
 [1609] 0.888840973 0.103830121 0.007328918 0.028840397 0.138430744 0.832728863
 [1615] 0.020264316 0.163182929 0.816552758 0.583669424 0.396525532 0.019805053
 [1621] 0.014381645 0.100956112 0.884662271 0.010131441 0.543276012 0.446592540
 [1627] 0.732982099 0.226859957 0.040157892 0.008524030 0.073978625 0.917497396
 [1633] 0.907686114 0.084780671 0.007533199 0.017319564 0.194036245 0.788644195
 [1639] 0.957815647 0.036064979 0.006119343 0.905191600 0.087298378 0.007510022
 [1645] 0.904501200 0.086273931 0.009224881 0.666263878 0.310317814 0.023418268
 [1651] 0.775567949 0.209548920 0.014883123 0.066242032 0.327058256 0.606699705
 [1657] 0.025679393 0.188688979 0.785631657 0.027313149 0.220520735 0.752166152
 [1663] 0.032942399 0.203407854 0.763649762 0.047791768 0.275486439 0.676721752
 [1669] 0.055625170 0.282957584 0.661417246 0.833636463 0.150200710 0.016162837
 [1675] 0.014912320 0.116348200 0.868739426 0.116331376 0.513218164 0.370450467
 [1681] 0.105791479 0.514783800 0.379424721 0.366791546 0.313991755 0.319216639
 [1687] 0.099029504 0.357498854 0.543471575 0.015781336 0.120378278 0.863840401
 [1693] 0.833185732 0.147198468 0.019615773 0.505107760 0.356420100 0.138472125
 [1699] 0.023668425 0.201704741 0.774626851 0.033957765 0.252014965 0.714027286
 [1705] 0.941758692 0.050907712 0.007333637 0.051571801 0.241774008 0.706654131
 [1711] 0.031625025 0.184068099 0.784306824 0.223043516 0.760096669 0.016859766
 [1717] 0.314101219 0.647912621 0.037986148 0.696336567 0.292480081 0.011183375
 [1723] 0.225082919 0.719381392 0.055535674 0.004298332 0.073674925 0.922026813
 [1729] 0.153329849 0.807269931 0.039400190 0.235518441 0.665910602 0.098570950
 [1735] 0.173652261 0.793779850 0.032567911 0.484516263 0.500272274 0.015211469
 [1741] 0.544631362 0.426247269 0.029121408 0.437057167 0.542163014 0.020779843
 [1747] 0.221626714 0.488916188 0.289457083 0.501918733 0.465635806 0.032445449
 [1753] 0.324841619 0.650965750 0.024192607 0.548754752 0.426925302 0.024319977
 [1759] 0.004548352 0.069367364 0.926084220 0.426225871 0.557422996 0.016351089
 [1765] 0.581604004 0.376915216 0.041480776 0.017205697 0.083036035 0.899758220
 [1771] 0.491345882 0.493299723 0.015354374 0.451073438 0.483918548 0.065008029
 [1777] 0.416836590 0.534693182 0.048470210 0.611058176 0.378051877 0.010889960
 [1783] 0.624530375 0.342676610 0.032793060 0.298826277 0.666741550 0.034432214
 [1789] 0.033523627 0.355379015 0.611097336 0.421520978 0.524272323 0.054206725
 [1795] 0.030927615 0.324994326 0.644078076 0.405082792 0.577170193 0.017746983
 [1801] 0.486832112 0.476234823 0.036933109 0.021691490 0.240102574 0.738205910
 [1807] 0.012512659 0.225360155 0.762127161 0.026739324 0.208682790 0.764577866
 [1813] 0.694249094 0.296188742 0.009562148 0.543384135 0.428025901 0.028589970
 [1819] 0.404792160 0.581812263 0.013395580 0.010428165 0.109159835 0.880412042
 [1825] 0.512085497 0.472914219 0.015000287 0.369354278 0.587532163 0.043113541
 [1831] 0.529032588 0.330224812 0.140742600 0.482413232 0.496722907 0.020863790
 [1837] 0.488264710 0.491015047 0.020720290 0.637012482 0.349620879 0.013366582
 [1843] 0.646181226 0.313577473 0.040241316 0.724152029 0.244479179 0.031368852
 [1849] 0.718178630 0.219348952 0.062472399 0.653576732 0.331733078 0.014690221
 [1855] 0.697819412 0.287359864 0.014820737 0.137313277 0.313724130 0.548962593
 [1861] 0.698265970 0.208727553 0.093006440 0.747098505 0.222474754 0.030426739
 [1867] 0.786896765 0.202794537 0.010308691 0.476297408 0.310379863 0.213322774
 [1873] 0.808991849 0.183863625 0.007144568 0.725177109 0.250209123 0.024613807
 [1879] 0.596890211 0.362705946 0.040403809 0.790840089 0.198393688 0.010766200
 [1885] 0.475153774 0.434093595 0.090752661 0.672297657 0.280214101 0.047488242
 [1891] 0.859405339 0.128502101 0.012092628 0.087570019 0.315062791 0.597367227
 [1897] 0.745701551 0.239602029 0.014696395 0.705282748 0.265899301 0.028818002
 [1903] 0.718976974 0.256852299 0.024170686 0.676223695 0.300562888 0.023213442
 [1909] 0.615195811 0.202331156 0.182473004 0.669385731 0.254149020 0.076465294
 [1915] 0.087090887 0.349854350 0.563054740 0.642137170 0.283500791 0.074362092
 [1921] 0.648265958 0.322752267 0.028981768 0.412350148 0.256861210 0.330788642
 [1927] 0.011670334 0.378661096 0.609668553 0.778352618 0.202466846 0.019180546
 [1933] 0.783851743 0.199247509 0.016900742 0.492400110 0.400559694 0.107040159
 [1939] 0.559220612 0.421954125 0.018825289 0.630053103 0.347442240 0.022504659
 [1945] 0.758305669 0.225550160 0.016144151 0.033141021 0.181200966 0.785658002
 [1951] 0.734044373 0.247396469 0.018559106 0.721794605 0.264498919 0.013706440
 [1957] 0.553894639 0.416084021 0.030021377 0.704575062 0.280670762 0.014754188
 [1963] 0.784605265 0.202701330 0.012693409 0.364058197 0.242194057 0.393747807
 [1969] 0.502647519 0.334605515 0.162746951 0.569404185 0.380258024 0.050337788
 [1975] 0.697757065 0.265312910 0.036930025 0.547018111 0.229316875 0.223664999
 [1981] 0.642048895 0.341428965 0.016522126 0.719700396 0.253463775 0.026835863
 [1987] 0.701393843 0.242855445 0.055750675 0.769265771 0.213955358 0.016778814
 [1993] 0.689460635 0.243378252 0.067161143 0.851526499 0.133115768 0.015357792
 [1999] 0.374183774 0.326841265 0.298974991 0.688225508 0.294388175 0.017386310
 [2005] 0.697292805 0.290245801 0.012461459 0.712878227 0.256413788 0.030707981
 [2011] 0.551790059 0.311600029 0.136609957 0.761020362 0.216008246 0.022971401
 [2017] 0.029637817 0.185390055 0.784972131 0.591847301 0.373991072 0.034161657
 [2023] 0.017979980 0.132802248 0.849217772 0.718392730 0.231942534 0.049664702
 [2029] 0.625083208 0.335215837 0.039700944 0.005359347 0.061528239 0.933112442
 [2035] 0.690653384 0.277063817 0.032282811 0.679824829 0.267588049 0.052587099
 [2041] 0.483124286 0.254323125 0.262552559 0.606088638 0.380489945 0.013421422
 [2047] 0.041287418 0.184351146 0.774361432 0.734554648 0.241034150 0.024411196
 [2053] 0.576634109 0.283820003 0.139545918 0.517869115 0.457021803 0.025109112
 [2059] 0.630589247 0.356545538 0.012865280 0.573441625 0.198487729 0.228070661
 [2065] 0.034592502 0.271100819 0.694306672 0.229134277 0.282665551 0.488200247
 [2071] 0.505351424 0.450729698 0.043918863 0.656518161 0.301593244 0.041888531
 [2077] 0.019458406 0.151604787 0.828936756 0.614280343 0.354140639 0.031579021
 [2083] 0.743561745 0.243615493 0.012822746 0.530840099 0.453619450 0.015540477
 [2089] 0.717552125 0.269667983 0.012779842 0.528729022 0.458300710 0.012970277
 [2095] 0.616581976 0.368080765 0.015337215 0.763525188 0.203247458 0.033227362
 [2101] 0.811458290 0.170570150 0.017971629 0.736379683 0.243084565 0.020535793
 [2107] 0.825493038 0.125058562 0.049448375 0.636283398 0.332514673 0.031201920
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[18655] 0.460235685 0.378245831 0.161518469 0.141304657 0.227250263 0.631445050
[18661] 0.474798173 0.360931724 0.164270148 0.142152861 0.405159146 0.452687979
[18667] 0.082334578 0.134724423 0.782940984 0.012148732 0.155613840 0.832237422
[18673] 0.181835264 0.271170765 0.546993971 0.065002039 0.192705482 0.742292464
[18679] 0.020255260 0.108745277 0.870999455 0.321745127 0.391458124 0.286796778
[18685] 0.051890604 0.174916983 0.773192406 0.442561924 0.400200427 0.157237679
[18691] 0.093979068 0.528815806 0.377205104 0.048034493 0.365359664 0.586605847
[18697] 0.006575502 0.067070007 0.926354527 0.067458928 0.437815845 0.494725257
[18703] 0.301337302 0.556503654 0.142159075 0.048119094 0.383246064 0.568634868
[18709] 0.037271623 0.201116592 0.761611819 0.014590639 0.124238461 0.861170888
[18715] 0.120567434 0.468857348 0.410575241 0.017049406 0.139521897 0.843428731
[18721] 0.010172173 0.066568688 0.923259139 0.055096291 0.289752722 0.655151010
[18727] 0.014598405 0.103036821 0.882364750 0.024684891 0.445865154 0.529449999
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[18739] 0.068080425 0.494368911 0.437550664 0.008287883 0.050091334 0.941620827
[18745] 0.095249325 0.459343284 0.445407361 0.025795443 0.503484190 0.470720381
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[18757] 0.008353009 0.214073747 0.777573228 0.271357208 0.300502181 0.428140670
[18763] 0.158695310 0.501460254 0.339844406 0.438658804 0.456372827 0.104968369
[18769] 0.042330317 0.263786137 0.693883538 0.026182180 0.212829649 0.760988116
[18775] 0.361855805 0.495297730 0.142846480 0.018756311 0.153177783 0.828065872
[18781] 0.167118028 0.460452735 0.372429222 0.689998567 0.280751288 0.029250138
[18787] 0.303782016 0.452537894 0.243680120 0.140141025 0.347728848 0.512130141
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[18799] 0.018568844 0.165051475 0.816379666 0.056708932 0.278890073 0.664400995
[18805] 0.474806339 0.358065546 0.167128146 0.499475211 0.416770339 0.083754398
[18811] 0.017671254 0.137019783 0.845308959 0.008034321 0.117585175 0.874380469
[18817] 0.094614975 0.369871378 0.535513639 0.038029511 0.254977733 0.706992745
[18823] 0.193533346 0.438028574 0.368438035 0.051298585 0.369182855 0.579518557
[18829] 0.484070897 0.332487851 0.183441296 0.424196273 0.421759993 0.154043689
[18835] 0.210607395 0.634482026 0.154910564 0.018413236 0.176731646 0.804855108
[18841] 0.729215503 0.233700156 0.037084367 0.541406691 0.338298619 0.120294690
[18847] 0.069276869 0.331663728 0.599059403 0.024084689 0.202527776 0.773387492
[18853] 0.005921796 0.468583614 0.525494576 0.038954522 0.274366528 0.686679006
[18859] 0.020100186 0.206306562 0.773593307 0.027069340 0.239789829 0.733140826
[18865] 0.099739082 0.410806477 0.489454508 0.127273187 0.407793909 0.464932859
[18871] 0.230796561 0.578789294 0.190414146 0.012242192 0.152675793 0.835081995
[18877] 0.583901167 0.399147809 0.016951004 0.789324224 0.173021883 0.037653860
[18883] 0.721274018 0.233673677 0.045052283 0.714227259 0.235252395 0.050520293
[18889] 0.858205259 0.131956846 0.009837926 0.814237535 0.168826312 0.016936174
[18895] 0.129147470 0.203951627 0.666900933 0.688358068 0.280730784 0.030911116
[18901] 0.803964734 0.178853139 0.017182134 0.512777090 0.337400138 0.149822742
[18907] 0.653427660 0.280907810 0.065664589 0.639657855 0.317148983 0.043193154
[18913] 0.587557316 0.257649958 0.154792756 0.729876339 0.248582363 0.021541348
[18919] 0.723571062 0.208857492 0.067571446 0.675205112 0.262591898 0.062202983
[18925] 0.836259544 0.152747571 0.010992853 0.435220957 0.369769335 0.195009723
[18931] 0.724550664 0.236852542 0.038596772 0.503954411 0.278450698 0.217594877
[18937] 0.431946754 0.343147069 0.224906191 0.572785199 0.280337393 0.146877423
[18943] 0.473029405 0.280449122 0.246521503 0.806775749 0.180947065 0.012277190
[18949] 0.722484648 0.261189520 0.016325863 0.685394168 0.270871282 0.043734502
[18955] 0.779781997 0.192325905 0.027892061 0.086467519 0.229515210 0.684017301
[18961] 0.680557787 0.266190708 0.053251445 0.437368274 0.359689176 0.202942535
[18967] 0.817406178 0.167598099 0.014995694 0.062271755 0.752410829 0.185317457
[18973] 0.614366055 0.343131036 0.042502899 0.807673275 0.165771946 0.026554776
[18979] 0.774788260 0.178891629 0.046320081 0.267635137 0.280619442 0.451745480
[18985] 0.693840384 0.260602415 0.045557179 0.746353805 0.227396801 0.026249390
[18991] 0.439988166 0.495738715 0.064273134 0.229040623 0.134548530 0.636410892
[18997] 0.571781754 0.402273893 0.025944382 0.815404892 0.160819829 0.023775322
[19003] 0.436296761 0.472440541 0.091262676 0.452960819 0.372316927 0.174722224
[19009] 0.692074418 0.255889475 0.052036118 0.879275262 0.108792759 0.011932004
[19015] 0.650253892 0.283237398 0.066508710 0.099805757 0.164211795 0.735982478
[19021] 0.836618185 0.153826520 0.009555326 0.734050453 0.240448475 0.025501052
[19027] 0.817511082 0.170544446 0.011944424 0.867398620 0.124816954 0.007784366
[19033] 0.692005754 0.229570791 0.078423463 0.833952069 0.148872465 0.017175494
[19039] 0.809592128 0.157952443 0.032455433 0.763332844 0.208207324 0.028459879
[19045] 0.898414433 0.088207394 0.013378154 0.555467844 0.318254650 0.126277462
[19051] 0.734441340 0.239472136 0.026086586 0.843336403 0.144534543 0.012129037
[19057] 0.797242820 0.189542577 0.013214647 0.574172914 0.331707120 0.094119973
[19063] 0.920842707 0.075429164 0.003728170 0.457809538 0.449176282 0.093014158
[19069] 0.786655009 0.192755744 0.020589240 0.213284165 0.252195269 0.534520566
[19075] 0.736335576 0.194893256 0.068771206 0.397468150 0.414262712 0.188269123
[19081] 0.454937011 0.298841864 0.246221140 0.286047995 0.300195575 0.413756460
[19087] 0.578126907 0.398433268 0.023439810 0.793275476 0.169298738 0.037425820
[19093] 0.869963467 0.120409705 0.009626785 0.841986060 0.146993741 0.011020176
[19099] 0.448320150 0.242336169 0.309343696 0.690502107 0.300471067 0.009026834
[19105] 0.514949083 0.348394334 0.136656553 0.824640751 0.159466371 0.015892804
[19111] 0.397526592 0.339209586 0.263263822 0.825400829 0.155814916 0.018784216
[19117] 0.794179142 0.176936954 0.028883908 0.691199005 0.245067328 0.063733689
[19123] 0.867438912 0.122606844 0.009954249 0.691776037 0.251838923 0.056385044
[19129] 0.791461766 0.192400739 0.016137525 0.076373741 0.226505026 0.697121263
[19135] 0.866820276 0.108086109 0.025093650 0.741442621 0.230598643 0.027958717
[19141] 0.401408106 0.395488292 0.203103617 0.828738928 0.141619563 0.029641535
[19147] 0.804177105 0.183672920 0.012149910 0.861052692 0.128830299 0.010117013
[19153] 0.453389347 0.507561684 0.039049007 0.765396714 0.221670970 0.012932321
[19159] 0.708184242 0.259135604 0.032680176 0.892776191 0.096842214 0.010381586
[19165] 0.788652718 0.179969490 0.031377770 0.759235203 0.220229983 0.020534813
[19171] 0.834868193 0.129425064 0.035706740 0.834068060 0.152593017 0.013338942
[19177] 0.777281582 0.192380354 0.030338010 0.870905697 0.120749034 0.008345287
[19183] 0.872880280 0.118800119 0.008319578 0.821438193 0.153346717 0.025215134
[19189] 0.848100007 0.136888862 0.015011162 0.465330780 0.295791507 0.238877699
[19195] 0.647434533 0.255837530 0.096727915 0.347117484 0.351256013 0.301626533
[19201] 0.566074610 0.259785622 0.174139723 0.804163933 0.156463221 0.039372854
[19207] 0.683701217 0.292471498 0.023827313 0.683870256 0.261305064 0.054824755
[19213] 0.861504912 0.127793193 0.010701825 0.753918052 0.217268124 0.028813846
[19219] 0.518120408 0.336465150 0.145414457 0.427328199 0.339554101 0.233117655
[19225] 0.756965518 0.205812544 0.037221894 0.856395245 0.135496214 0.008108542
[19231] 0.661639869 0.234936506 0.103423633 0.870907068 0.096397907 0.032695070
[19237] 0.770014942 0.189172849 0.040812265 0.890740752 0.101405852 0.007853349
[19243] 0.845808268 0.134099841 0.020091904 0.879313648 0.105381615 0.015304797
[19249] 0.164724886 0.162296653 0.672978461 0.797489464 0.188268676 0.014241870
[19255] 0.633653641 0.333103269 0.033243041 0.830325663 0.158368424 0.011305945
[19261] 0.738838255 0.240778714 0.020382976 0.585320890 0.298643470 0.116035588
[19267] 0.598621428 0.258525848 0.142852738 0.731860340 0.247288764 0.020850912
[19273] 0.752828419 0.212479979 0.034691587 0.686815083 0.252035648 0.061149213
[19279] 0.758494556 0.202069968 0.039435476 0.406996816 0.565819621 0.027183594
[19285] 0.663144588 0.268140078 0.068715297 0.188840955 0.351107121 0.460051864
[19291] 0.633069396 0.292327076 0.074603543 0.498418212 0.359090000 0.142491788
[19297] 0.748227537 0.213009819 0.038762674 0.580041230 0.337376982 0.082581773
[19303] 0.720205963 0.250353366 0.029440653 0.353122264 0.465898931 0.180978820
[19309] 0.710754097 0.269947916 0.019297915 0.547562599 0.339854717 0.112582617
[19315] 0.793262541 0.195635200 0.011102231 0.869716525 0.123633549 0.006649893
[19321] 0.848225892 0.132405326 0.019368831 0.096737683 0.190703258 0.712559044
[19327] 0.646934032 0.332853317 0.020212611 0.729398072 0.233200207 0.037401758
[19333] 0.723455071 0.242007405 0.034537472 0.776417732 0.206377268 0.017205024
[19339] 0.849423110 0.139138818 0.011438055 0.726711273 0.248729795 0.024558933
[19345] 0.766415119 0.207523078 0.026061812 0.900958776 0.094024606 0.005016671
[19351] 0.498602360 0.435988992 0.065408684 0.825233877 0.165649965 0.009116139
[19357] 0.839109063 0.146955654 0.013935212 0.704350948 0.247707471 0.047941580
[19363] 0.477531612 0.460853100 0.061615311 0.668319881 0.312776178 0.018903913
[19369] 0.774871528 0.206154779 0.018973701 0.749263227 0.199690923 0.051045824
[19375] 0.826672077 0.164624989 0.008702899 0.684524298 0.259293407 0.056182306
[19381] 0.749194801 0.231387258 0.019418007 0.869152069 0.120801374 0.010046529
[19387] 0.770646155 0.212378860 0.016975021 0.748323917 0.224168733 0.027507357
[19393] 0.446173400 0.351469785 0.202356771 0.759561419 0.208787501 0.031651095
[19399] 0.603837430 0.353391141 0.042771406 0.534014106 0.332387954 0.133597896
[19405] 0.233420148 0.271280617 0.495299190 0.695870221 0.259916365 0.044213396
[19411] 0.808626711 0.181889236 0.009483987 0.808508217 0.178572923 0.012918838
[19417] 0.350704968 0.498340279 0.150954738 0.265281737 0.544662595 0.190055683
[19423] 0.591096818 0.326302320 0.082600854 0.729002714 0.228654876 0.042342447
[19429] 0.312269598 0.359205931 0.328524500 0.809816957 0.176079229 0.014103833
[19435] 0.851044714 0.139388219 0.009567056 0.893988431 0.096953757 0.009057832
[19441] 0.922750950 0.068077020 0.009172069 0.551696301 0.319326133 0.128977597
[19447] 0.789955795 0.190852031 0.019192109 0.662670374 0.255629450 0.081700183
[19453] 0.441326797 0.312530696 0.246142492 0.530677855 0.400796056 0.068526097
[19459] 0.895883322 0.097950295 0.006166383 0.705763996 0.267507493 0.026728489
[19465] 0.862749398 0.129264563 0.007986088 0.452971011 0.378472567 0.168556437
[19471] 0.847578645 0.139991462 0.012429855 0.751752317 0.211070046 0.037177652
[19477] 0.738735974 0.227875262 0.033388749 0.891379714 0.101709478 0.006910745
[19483] 0.744207561 0.234320670 0.021471761 0.663854539 0.280167252 0.055978205
[19489] 0.478286028 0.334149927 0.187564015 0.730086386 0.246055722 0.023857879
[19495] 0.771363616 0.204477057 0.024159288 0.589053035 0.271281123 0.139665872
[19501] 0.547343135 0.290027589 0.162629247 0.204764903 0.317189336 0.478045732
[19507] 0.647187948 0.248893037 0.103919022 0.839935839 0.149042204 0.011021963
[19513] 0.827671528 0.154923022 0.017405456 0.841445744 0.145204678 0.013349597
[19519] 0.783303440 0.188103557 0.028592976 0.917550504 0.065730229 0.016719263
[19525] 0.738834321 0.232193053 0.028972629 0.451382458 0.356196493 0.192421094
[19531] 0.467412114 0.290784985 0.241802916 0.248212904 0.262709469 0.489077657
[19537] 0.813616097 0.173356697 0.013027265 0.833538890 0.151926711 0.014534417
[19543] 0.385250449 0.392624497 0.222125024 0.876602411 0.112260453 0.011137104
[19549] 0.538714409 0.346481264 0.114804290 0.863108456 0.128125206 0.008766351
[19555] 0.781429768 0.196386740 0.022183435 0.174180463 0.234693691 0.591125846
[19561] 0.653659344 0.215177551 0.131163120 0.299231291 0.401359439 0.299409240
[19567] 0.762547195 0.131651029 0.105801709 0.915630758 0.071029253 0.013340033
[19573] 0.748491108 0.210756525 0.040752333 0.816516101 0.158156395 0.025327498
[19579] 0.144106939 0.794169188 0.061723899 0.749147356 0.218608215 0.032244477
[19585] 0.831119895 0.161124706 0.007755383 0.923173904 0.071995124 0.004830923
[19591] 0.080002025 0.697674811 0.222323209 0.560645223 0.316331357 0.123023413
[19597] 0.176358774 0.273351908 0.550289333 0.844670415 0.137030452 0.018299108
[19603] 0.638860941 0.302166522 0.058972515 0.134641901 0.150873482 0.714484632
[19609] 0.677322388 0.205092072 0.117585562 0.649404705 0.295390844 0.055204492
[19615] 0.829912603 0.145108387 0.024979023 0.372765362 0.374157488 0.253077120
[19621] 0.734862030 0.247618392 0.017519590 0.311717123 0.408991545 0.279291302
[19627] 0.648072302 0.276929915 0.074997745 0.438563794 0.268609822 0.292826325
[19633] 0.839579403 0.127517179 0.032903463 0.770712495 0.201627403 0.027660165
[19639] 0.841404557 0.147012874 0.011582609 0.691997230 0.224311605 0.083691172
[19645] 0.718251705 0.256688207 0.025060123 0.478761822 0.356573135 0.164664999
[19651] 0.519818127 0.236868575 0.243313283 0.783355355 0.193052202 0.023592448
[19657] 0.783667266 0.196541265 0.019791482 0.617322624 0.275037467 0.107639924
[19663] 0.448052049 0.448091894 0.103856049 0.416366428 0.343581885 0.240051702
[19669] 0.887665451 0.106828123 0.005506391 0.852043092 0.118867852 0.029089017
[19675] 0.846068203 0.135258317 0.018673524 0.741108358 0.237561271 0.021330377
[19681] 0.781487048 0.199003100 0.019509871 0.674770832 0.268829882 0.056399267
[19687] 0.260064363 0.328020155 0.411915511 0.485580266 0.438587308 0.075832427
[19693] 0.337374479 0.423505455 0.239120111 0.806295097 0.149473175 0.044231758
[19699] 0.792613387 0.186289996 0.021096623 0.134110600 0.305862129 0.560027301
[19705] 0.510555446 0.278800100 0.210644439 0.866927683 0.114218578 0.018853785
[19711] 0.377399772 0.455561727 0.167038500 0.830091000 0.152962044 0.016946940
[19717] 0.815040052 0.173405915 0.011554055 0.774273276 0.210251227 0.015475492
[19723] 0.705013633 0.235367402 0.059618987 0.472198695 0.280677825 0.247123495
[19729] 0.830760539 0.156272858 0.012966542 0.720264852 0.236060813 0.043674305
[19735] 0.111535512 0.305355847 0.583108664 0.787664711 0.188772872 0.023562437
[19741] 0.459661186 0.440030873 0.100307956 0.581896424 0.291183382 0.126920238
[19747] 0.843848050 0.143998012 0.012153995 0.666561544 0.248873293 0.084565170
[19753] 0.691618681 0.276222408 0.032158863 0.636877894 0.336958468 0.026163595
[19759] 0.131015643 0.181390703 0.687593639 0.333296359 0.526092112 0.140611500
[19765] 0.412813067 0.455985367 0.131201506 0.397289157 0.530833244 0.071877584
[19771] 0.867552400 0.123708434 0.008739116 0.055351309 0.116925463 0.827723205
[19777] 0.722886384 0.253479689 0.023633862 0.539523900 0.317522377 0.142953679
[19783] 0.424191654 0.425774962 0.150033414 0.417790025 0.410548151 0.171661824
[19789] 0.473865926 0.291191131 0.234942913 0.736795366 0.246189833 0.017014792
[19795] 0.849326372 0.133644447 0.017029161 0.858277678 0.131728724 0.009993551
[19801] 0.713238418 0.253779560 0.032981995 0.761285782 0.208549574 0.030164661
[19807] 0.337545007 0.251950622 0.410504401 0.592466712 0.302383095 0.105150193
[19813] 0.601737022 0.285004556 0.113258369 0.778173923 0.197294340 0.024531718
[19819] 0.858812630 0.125178307 0.016009042 0.831350207 0.158412948 0.010236857
[19825] 0.542978406 0.423952073 0.033069517 0.854020000 0.135982737 0.009997291
[19831] 0.247449964 0.402128100 0.350421935 0.251695246 0.378337383 0.369967341
[19837] 0.424241006 0.296053618 0.279705405 0.329866767 0.373844892 0.296288371
[19843] 0.734989166 0.227994725 0.037016131 0.792484522 0.180203706 0.027311774
[19849] 0.638257623 0.232912302 0.128830090 0.759481668 0.221255839 0.019262465
[19855] 0.309451878 0.334139705 0.356408447 0.734892309 0.222787187 0.042320509
[19861] 0.144927189 0.341115028 0.513957798 0.827429473 0.160540342 0.012030201
[19867] 0.677895188 0.232527912 0.089576915 0.466491878 0.331334323 0.202173769
[19873] 0.770664394 0.206738546 0.022597071 0.808817804 0.181633025 0.009549093
[19879] 0.654449880 0.272722542 0.072827570 0.706715167 0.276546180 0.016738662
[19885] 0.411385596 0.396851003 0.191763446 0.617374063 0.346458167 0.036167778
[19891] 0.563938677 0.281811297 0.154250041 0.220374152 0.619102895 0.160522968
[19897] 0.840016305 0.147770166 0.012213472 0.647702575 0.334556669 0.017740767
[19903] 0.820330381 0.148476288 0.031193322 0.309886754 0.529509783 0.160603464
[19909] 0.343111128 0.355128288 0.301760584 0.579209208 0.341709793 0.079080991
[19915] 0.143246487 0.190286070 0.666467488 0.510729492 0.333715916 0.155554608
[19921] 0.423679322 0.337784261 0.238536462 0.687851250 0.263111234 0.049037494
[19927] 0.617803693 0.278483033 0.103713229 0.781146228 0.203018531 0.015835304
[19933] 0.395704806 0.432744265 0.171550959 0.778048396 0.173268616 0.048682984
[19939] 0.439952791 0.422065347 0.137981817 0.408415169 0.409686029 0.181898862
[19945] 0.805198073 0.175781891 0.019020034 0.581861258 0.349363804 0.068774968
[19951] 0.555771470 0.386146128 0.058082402 0.581408441 0.388125122 0.030466432
[19957] 0.853245854 0.135192961 0.011561167 0.744221091 0.195401564 0.060377304
[19963] 0.725664437 0.176059291 0.098276272 0.640247285 0.332127601 0.027625086
[19969] 0.716961026 0.258095682 0.024943350 0.359604627 0.406535655 0.233859777
[19975] 0.715623379 0.236146152 0.048230488 0.557114780 0.390892357 0.051992856
[19981] 0.919955850 0.072941773 0.007102440 0.701616466 0.209974840 0.088408716
[19987] 0.820433855 0.165897548 0.013668649 0.796892941 0.179713443 0.023393666
[19993] 0.237903714 0.211443618 0.550652683 0.426133513 0.339006543 0.234859899
[19999] 0.857387066 0.134650320 0.007962665 0.626569986 0.282028258 0.091401741
[20005] 0.778717279 0.182985708 0.038297012 0.660514235 0.285985768 0.053499993
[20011] 0.107665792 0.190334663 0.701999545 0.630487323 0.312349796 0.057162870
[20017] 0.726862133 0.247668222 0.025469711 0.052672744 0.095949292 0.851377904
[20023] 0.661693692 0.255799234 0.082507052 0.311384141 0.426008731 0.262607098
[20029] 0.700690985 0.259043783 0.040265221 0.262936950 0.404114842 0.332948238
[20035] 0.579346895 0.257780641 0.162872434 0.864839613 0.119187392 0.015972972
[20041] 0.233793154 0.470370501 0.295836329 0.717465222 0.260910779 0.021623990
[20047] 0.791239560 0.195338905 0.013421548 0.774901032 0.209370434 0.015728591
[20053] 0.251398653 0.435085565 0.313515812 0.900847852 0.087145045 0.012007118
[20059] 0.841687500 0.145246267 0.013066195 0.852124870 0.136823893 0.011051192
[20065] 0.698431551 0.270998567 0.030569848 0.268839091 0.317732036 0.413428903
[20071] 0.642672181 0.277290791 0.080037013 0.416478515 0.305734634 0.277786821
[20077] 0.601924241 0.334909141 0.063166633 0.835278153 0.152079195 0.012642724
[20083] 0.284921050 0.560126007 0.154952988 0.827967942 0.156246483 0.015785508
[20089] 0.787815034 0.201334164 0.010850819 0.673271358 0.262989104 0.063739575
[20095] 0.689681113 0.235656336 0.074662551 0.312334478 0.399289131 0.288376331
[20101] 0.672790527 0.300014853 0.027194634 0.061822157 0.084665485 0.853512347
[20107] 0.404745609 0.423812419 0.171441972 0.125590622 0.363575906 0.510833502
[20113] 0.272666425 0.353076130 0.374257445 0.502233863 0.330706269 0.167059913
[20119] 0.853292167 0.137586474 0.009121294 0.600471139 0.277996898 0.121531963
[20125] 0.867613435 0.121335872 0.011050756 0.354762614 0.192258447 0.452978939
[20131] 0.473252147 0.275045931 0.251701951 0.530785680 0.313286245 0.155928046
[20137] 0.759054840 0.223202884 0.017742310 0.689002037 0.279119760 0.031878207
[20143] 0.737086415 0.240610868 0.022302702 0.833240092 0.154281095 0.012478842
[20149] 0.219844311 0.390778303 0.389377385 0.829520226 0.160070106 0.010409625
[20155] 0.126050234 0.317964405 0.555985391 0.846287847 0.140759528 0.012952617
[20161] 0.582404494 0.265731037 0.151864439 0.601053119 0.314063638 0.084883228
[20167] 0.394361466 0.410914660 0.194723889 0.802610755 0.179717883 0.017671440
[20173] 0.806500971 0.171705335 0.021793654 0.819612384 0.170107797 0.010279810
[20179] 0.837599635 0.147415474 0.014984923 0.704641938 0.262103528 0.033254515
[20185] 0.447616637 0.355032384 0.197350964 0.909297347 0.076147906 0.014554703
[20191] 0.454277486 0.281125098 0.264597386 0.519970477 0.194774419 0.285255104
[20197] 0.783282280 0.182033777 0.034683902 0.667658389 0.243829802 0.088511854
[20203] 0.715251803 0.253259033 0.031489156 0.493932277 0.367798209 0.138269469
[20209] 0.158729449 0.196254417 0.645016134 0.626926780 0.332528621 0.040544618
[20215] 0.695244730 0.274808288 0.029947007 0.763262749 0.161704659 0.075032629
[20221] 0.650927067 0.327060044 0.022012832 0.734549105 0.232429564 0.033021327
[20227] 0.818804920 0.154124826 0.027070217 0.806915522 0.181726620 0.011357897
[20233] 0.184642687 0.406076282 0.409281045 0.770225763 0.216858745 0.012915465
[20239] 0.795983255 0.181294739 0.022722036 0.895600617 0.095572986 0.008826376
[20245] 0.671238959 0.304230750 0.024530308 0.490503699 0.442658693 0.066837542
[20251] 0.802854598 0.169933870 0.027211541 0.857855678 0.125119105 0.017025210
[20257] 0.602019250 0.331974119 0.066006608 0.676497042 0.173984438 0.149518535
[20263] 0.643547773 0.338774145 0.017678065 0.865976989 0.124495827 0.009527208
[20269] 0.820617735 0.165411249 0.013971070 0.692112207 0.289887607 0.018000223
[20275] 0.704489112 0.242031649 0.053479239 0.687777281 0.286161780 0.026060930
[20281] 0.518856108 0.361630231 0.119513623 0.750066459 0.235305071 0.014628498
[20287] 0.709985614 0.223855838 0.066158548 0.826928079 0.160308257 0.012763657
[20293] 0.788856030 0.196434781 0.014709255 0.373470992 0.334122419 0.292406529
[20299] 0.897430122 0.085020028 0.017549790 0.686681926 0.259669095 0.053649019
[20305] 0.808474243 0.173821211 0.017704589 0.938069403 0.058600649 0.003329970
[20311] 0.388400286 0.308250725 0.303348988 0.815776706 0.173817590 0.010405771
[20317] 0.460531354 0.419977993 0.119490683 0.025635192 0.827739298 0.146625534
[20323] 0.788414717 0.197271779 0.014313555 0.426297188 0.345662534 0.228040218
[20329] 0.429956853 0.379445642 0.190597519 0.200107485 0.184586123 0.615306377
[20335] 0.711965024 0.262591898 0.025443129 0.308597952 0.188064635 0.503337443
[20341] 0.341582119 0.285391718 0.373026162 0.514540136 0.360888273 0.124571562
[20347] 0.744296074 0.230525017 0.025178969 0.691001475 0.213318288 0.095680244
[20353] 0.753510714 0.223561674 0.022927621 0.407382637 0.371796012 0.220821366
[20359] 0.849168777 0.136351183 0.014480093 0.704529107 0.259403884 0.036067069
[20365] 0.212422669 0.331186771 0.456390560 0.746405303 0.217344984 0.036249742
[20371] 0.848696947 0.131726280 0.019576749 0.831061125 0.157025769 0.011913088
[20377] 0.724815249 0.259667516 0.015517190 0.876851916 0.113472201 0.009675931
[20383] 0.574395597 0.296176314 0.129428089 0.676591933 0.242735505 0.080672577
[20389] 0.141220734 0.268033266 0.590745986 0.200080916 0.339166552 0.460752517
[20395] 0.283794641 0.333566338 0.382639050 0.619432986 0.277260870 0.103306167
[20401] 0.880251527 0.109027810 0.010720596 0.723771751 0.238297418 0.037930846
[20407] 0.780693293 0.206949860 0.012356845 0.509828210 0.325902104 0.164269745
[20413] 0.898064315 0.095408052 0.006527599 0.665099680 0.220381260 0.114519097
[20419] 0.224448532 0.217377648 0.558173835 0.909797609 0.081338033 0.008864333
[20425] 0.744072378 0.243580252 0.012347376 0.819773853 0.165177569 0.015048585
[20431] 0.739184022 0.221358985 0.039456978 0.670632482 0.290220469 0.039146997
[20437] 0.548072398 0.331603795 0.120323755 0.530437768 0.334084183 0.135478020
[20443] 0.489433378 0.314820319 0.195746347 0.737366259 0.199331433 0.063302316
[20449] 0.778920650 0.203209624 0.017869687 0.597166240 0.220258996 0.182574734
[20455] 0.554433167 0.317353696 0.128213137 0.526583433 0.305022866 0.168393731
[20461] 0.343214631 0.328068316 0.328717053 0.437667578 0.363525629 0.198806748
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[20479] 0.857149899 0.121991202 0.020858882 0.579633474 0.348883212 0.071483344
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[20491] 0.817466080 0.157822281 0.024711654 0.760098636 0.213226467 0.026674949
[20497] 0.169180706 0.265376925 0.565442324 0.810123384 0.148406997 0.041469630
[20503] 0.695736408 0.266218543 0.038045049 0.907958806 0.087200209 0.004841001
[20509] 0.863767445 0.127108216 0.009124341 0.597186565 0.192587167 0.210226253
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[20527] 0.710679710 0.251351774 0.037968505 0.651794195 0.307068139 0.041137673
[20533] 0.545699716 0.293371022 0.160929248 0.396946400 0.560205519 0.042848088
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[20551] 0.864883602 0.125419691 0.009696730 0.389307290 0.316078663 0.294614047
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[20581] 0.813349366 0.165866211 0.020784384 0.719666541 0.251255065 0.029078361
[20587] 0.270932257 0.531087399 0.197980344 0.481073976 0.318352133 0.200573951
[20593] 0.036226552 0.654490292 0.309283167 0.655958533 0.252249718 0.091791764
[20599] 0.145329267 0.294089109 0.560581565 0.781879663 0.207031593 0.011088693
[20605] 0.420248717 0.314540654 0.265210629 0.715982616 0.239961475 0.044055883
[20611] 0.791587532 0.187666252 0.020746209 0.560112715 0.329036415 0.110850886
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[20623] 0.722952127 0.252760172 0.024287671 0.703346789 0.238208085 0.058445137
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[20635] 0.636352718 0.252316177 0.111331165 0.753781080 0.221820652 0.024398237
[20641] 0.908216000 0.085395820 0.006388220 0.657043576 0.259128243 0.083828196
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[20659] 0.787346363 0.169620037 0.043033592 0.736937463 0.209406301 0.053656194
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[20683] 0.487743407 0.327525944 0.184730649 0.889890432 0.100473017 0.009636591
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[20743] 0.340444952 0.379711449 0.279843628 0.748025239 0.235457003 0.016517710
[20749] 0.169374213 0.771866441 0.058759347 0.728749335 0.231040463 0.040210199
[20755] 0.064388596 0.791171610 0.144439802 0.300697863 0.297617376 0.401684821
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[20803] 0.791478157 0.194249868 0.014271975 0.878585815 0.108968236 0.012445967
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[20845] 0.523356974 0.397701710 0.078941368 0.352625102 0.256356239 0.391018629
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[20923] 0.887392759 0.101758637 0.010848616 0.939681590 0.055614207 0.004704218
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[20947] 0.614694357 0.273401022 0.111904621 0.798196971 0.142941818 0.058861218
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[20959] 0.735349536 0.234039456 0.030611029 0.656023026 0.269053847 0.074923091
[20965] 0.774425209 0.199826971 0.025747800 0.674130619 0.262531757 0.063337572
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[20989] 0.231828138 0.622777641 0.145394191 0.765596211 0.199833781 0.034570009
[20995] 0.788060367 0.193868712 0.018070940 0.905809522 0.089045495 0.005144917
[21001] 0.634243071 0.252624959 0.113131948 0.742134392 0.201682553 0.056183062
[21007] 0.747883022 0.227644190 0.024472812 0.879885912 0.111427866 0.008686163
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[22105] 0.060362767 0.448090523 0.491546690 0.161386207 0.595526695 0.243087143
[22111] 0.139472142 0.380926907 0.479600996 0.023011956 0.237921640 0.739066422
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[22123] 0.041812453 0.444653809 0.513533711 0.039712794 0.562203825 0.398083419
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[34015] 0.849187672 0.141804248 0.009008057 0.832288384 0.154690415 0.013021216
[34021] 0.081501111 0.355451226 0.563047647 0.666966259 0.299874425 0.033159293
[34027] 0.681547523 0.273577422 0.044875037 0.050655559 0.282090902 0.667253554
[34033] 0.745431125 0.188619554 0.065949336 0.448693067 0.462051809 0.089255102
[34039] 0.779805005 0.178749681 0.041445307 0.736483991 0.213513359 0.050002638
[34045] 0.047796108 0.684974492 0.267229408 0.692395806 0.267440528 0.040163688
[34051] 0.192575812 0.210647330 0.596776903 0.738188267 0.245655119 0.016156675
[34057] 0.713486135 0.257083565 0.029430237 0.013291482 0.201140866 0.785567641
[34063] 0.660217583 0.312306792 0.027475592 0.690928221 0.249578848 0.059492905
[34069] 0.039422218 0.219728038 0.740849793 0.370240927 0.311295420 0.318463624
[34075] 0.787124574 0.194669053 0.018206345 0.847253978 0.142709658 0.010036410
[34081] 0.547928452 0.313995868 0.138075709 0.718373954 0.259493828 0.022132223
[34087] 0.658186436 0.307467133 0.034346443 0.531605482 0.300005674 0.168388814
[34093] 0.756998777 0.226164982 0.016836269 0.570821822 0.351349145 0.077828996
[34099] 0.679474950 0.254416972 0.066108115 0.589679122 0.341153294 0.069167607
[34105] 0.789050102 0.196694985 0.014254901 0.057520945 0.250201851 0.692277193
[34111] 0.685000956 0.281282455 0.033716604 0.830430925 0.152261227 0.017307794
[34117] 0.017349394 0.124593325 0.858057261 0.329870880 0.273281753 0.396847397
[34123] 0.733993232 0.218497083 0.047509715 0.630647779 0.293872327 0.075479880
[34129] 0.797650754 0.185932562 0.016416663 0.835122705 0.153924450 0.010952880
[34135] 0.736090243 0.247189596 0.016720200 0.019929633 0.200898752 0.779171646
[34141] 0.742531538 0.239961699 0.017506814 0.582130849 0.310899615 0.106969565
[34147] 0.088189811 0.294726759 0.617083430 0.040040269 0.179642171 0.780317545
[34153] 0.043002367 0.142546475 0.814451218 0.370871514 0.364783913 0.264344573
[34159] 0.730928540 0.247943461 0.021128001 0.041306525 0.235922411 0.722771049
[34165] 0.598540664 0.352459073 0.049000226 0.532227516 0.415224612 0.052547906
[34171] 0.361669719 0.381162345 0.257167935 0.027645281 0.158827350 0.813527405
[34177] 0.813774168 0.178644702 0.007581163 0.572140574 0.343320698 0.084538750
[34183] 0.759781957 0.228210449 0.012007574 0.573326588 0.268831432 0.157842010
[34189] 0.608116210 0.289542377 0.102341391 0.665527940 0.286489993 0.047982108
[34195] 0.784761369 0.188660026 0.026578547 0.830782950 0.161567882 0.007649222
[34201] 0.391484946 0.351139903 0.257375091 0.832363844 0.153130442 0.014505700
[34207] 0.791068077 0.192801371 0.016130559 0.564719141 0.308710486 0.126570374
[34213] 0.728171766 0.231027722 0.040800519 0.757603049 0.235702246 0.006694710
[34219] 0.727096558 0.257220566 0.015682872 0.853043437 0.132925063 0.014031545
[34225] 0.885227859 0.102884427 0.011887688 0.043383889 0.192265615 0.764350474
[34231] 0.461044520 0.420300364 0.118655160 0.027156942 0.263104051 0.709739029
[34237] 0.384982824 0.286180943 0.328836262 0.025992241 0.053212985 0.920794785
[34243] 0.025833543 0.179949537 0.794216931 0.280881584 0.312354386 0.406764060
[34249] 0.672970235 0.245093167 0.081936650 0.780464470 0.208151281 0.011384208
[34255] 0.030209815 0.088057846 0.881732285 0.565663993 0.316122741 0.118213266
[34261] 0.020483119 0.252023846 0.727493048 0.093086250 0.266118497 0.640795290
[34267] 0.705346465 0.272092372 0.022561127 0.018707389 0.172308668 0.808983922
[34273] 0.769524395 0.198888198 0.031587355 0.059505872 0.290298849 0.650195241
[34279] 0.745860159 0.226859048 0.027280744 0.647037625 0.312129468 0.040832929
[34285] 0.877057195 0.059061494 0.063881367 0.810276985 0.172907144 0.016815852
[34291] 0.004055759 0.141208887 0.854735374 0.119942814 0.457789510 0.422267705
[34297] 0.579807341 0.343104452 0.077088214 0.013335110 0.192120925 0.794543982
[34303] 0.006822235 0.075624444 0.917553306 0.009998632 0.087907210 0.902094185
[34309] 0.028102797 0.221176192 0.750721037 0.679800749 0.282835603 0.037363652
[34315] 0.613667548 0.307388276 0.078944199 0.853637159 0.137860641 0.008502231
[34321] 0.088532105 0.731962681 0.179505229 0.169583008 0.241271049 0.589145958
[34327] 0.042720083 0.241438523 0.715841353 0.603620768 0.299014837 0.097364388
[34333] 0.016980240 0.121406794 0.861612976 0.047880467 0.324432671 0.627686858
[34339] 0.057970513 0.359561116 0.582468390 0.032705933 0.208302468 0.758991599
[34345] 0.070172437 0.282684922 0.647142589 0.754991472 0.231195271 0.013813269
[34351] 0.687774897 0.209143251 0.103081897 0.089302734 0.416672200 0.494025081
[34357] 0.814647853 0.171629757 0.013722387 0.742573321 0.230724633 0.026702043
[34363] 0.066170812 0.345072567 0.588756561 0.013429628 0.206658974 0.779911339
[34369] 0.043969586 0.273539305 0.682491124 0.016991448 0.170410082 0.812598526
[34375] 0.031632084 0.241031155 0.727336824 0.009631940 0.040589087 0.949778914
[34381] 0.025227327 0.485374302 0.489398420 0.021818083 0.267361850 0.710820079
[34387] 0.026140615 0.195324704 0.778534710 0.721779585 0.262135446 0.016084986
[34393] 0.677114844 0.262235403 0.060649764 0.017979531 0.232326537 0.749693930
[34399] 0.005118046 0.207261667 0.787620246 0.009120123 0.162865371 0.828014493
[34405] 0.024783636 0.212246910 0.762969434 0.004698243 0.271909416 0.723392308
[34411] 0.178613007 0.108031124 0.713355899 0.347990841 0.408736080 0.243273154
[34417] 0.785349131 0.119986519 0.094664335 0.657963336 0.292667389 0.049369276
[34423] 0.627728105 0.349013299 0.023258580 0.009617885 0.076559857 0.913822293
[34429] 0.047740880 0.211071357 0.741187811 0.010812950 0.126279220 0.862907767
[34435] 0.028477952 0.104471564 0.867050529 0.045690097 0.259006351 0.695303559
[34441] 0.014602176 0.179864928 0.805532932 0.012203562 0.129418239 0.858378172
[34447] 0.115155488 0.411972255 0.472872257 0.019426614 0.218891621 0.761681736
[34453] 0.579616547 0.348965704 0.071417749 0.023535302 0.648221135 0.328243554
[34459] 0.579953909 0.303558439 0.116487637 0.657314241 0.149543181 0.193142608
[34465] 0.645041049 0.200096503 0.154862449 0.008691063 0.077154756 0.914154172
[34471] 0.029170688 0.224888921 0.745940328 0.056310568 0.142987460 0.800701976
[34477] 0.051790636 0.279462099 0.668747246 0.093176663 0.296104729 0.610718668
[34483] 0.048845179 0.385807574 0.565347254 0.021563547 0.211969420 0.766466975
[34489] 0.028450176 0.193949759 0.777600050 0.014110285 0.121727780 0.864161909
[34495] 0.005139519 0.116232462 0.878628016 0.015151395 0.179073960 0.805774629
[34501] 0.035877172 0.192804918 0.771317899 0.033625785 0.224232659 0.742141545
[34507] 0.040612821 0.227544442 0.731842697 0.038128864 0.124241531 0.837629557
[34513] 0.055155493 0.377725780 0.567118764 0.051551633 0.148036420 0.800411999
[34519] 0.078828998 0.790138125 0.131032884 0.044483699 0.118836604 0.836679757
[34525] 0.036770962 0.180938810 0.782290161 0.005015988 0.206031755 0.788952231
[34531] 0.064431049 0.185095251 0.750473738 0.040967204 0.144514531 0.814518273
[34537] 0.016662512 0.082172476 0.901165009 0.557411015 0.333116293 0.109472685
[34543] 0.023413671 0.275051266 0.701535046 0.020715401 0.347301990 0.631982625
[34549] 0.023361569 0.239655852 0.736982524 0.023570003 0.191011176 0.785418808
[34555] 0.032309573 0.564226210 0.403464168 0.027646324 0.116243236 0.856110513
[34561] 0.056701925 0.195253462 0.748044610 0.699322879 0.143539324 0.157137766
[34567] 0.020559127 0.114830874 0.864610016 0.013035185 0.174786523 0.812178314
[34573] 0.023787415 0.098843224 0.877369344 0.113101833 0.415578574 0.471319616
[34579] 0.012483888 0.114837922 0.872678220 0.786682308 0.191584781 0.021732964
[34585] 0.230809361 0.216300398 0.552890241 0.003513623 0.013397053 0.983089328
[34591] 0.004936408 0.116313376 0.878750265 0.035229187 0.182422295 0.782348573
[34597] 0.030339805 0.204763219 0.764896929 0.533470809 0.228791758 0.237737432
[34603] 0.036506146 0.396262556 0.567231297 0.012577833 0.162456408 0.824965715
[34609] 0.017271139 0.122390650 0.860338211 0.719238281 0.247287229 0.033474475
[34615] 0.029319873 0.172244370 0.798435748 0.005499311 0.263290584 0.731210053
[34621] 0.026428841 0.174864873 0.798706234 0.036976870 0.200964004 0.762059093
[34627] 0.030498598 0.209294096 0.760207295 0.018143984 0.145304531 0.836551487
[34633] 0.059391476 0.282743186 0.657865345 0.018289581 0.183021531 0.798688889
[34639] 0.046731692 0.247167304 0.706101000 0.019026799 0.234324127 0.746649086
[34645] 0.070846818 0.312930644 0.616222560 0.026076775 0.162478104 0.811445177
[34651] 0.008245492 0.120484747 0.871269763 0.005672005 0.066662244 0.927665770
[34657] 0.092812411 0.615636945 0.291550636 0.095824160 0.850031912 0.054143973
[34663] 0.156300232 0.588850379 0.254849434 0.210948899 0.723787665 0.065263391
[34669] 0.009449154 0.141696006 0.848854899 0.005229359 0.084681809 0.910088837
[34675] 0.003734499 0.084740661 0.911524832 0.011286798 0.399223447 0.589489758
[34681] 0.067491718 0.397165745 0.535342515 0.071353763 0.471834511 0.456811726
[34687] 0.036737226 0.058941487 0.904321253 0.008181420 0.367785454 0.624033153
[34693] 0.003602521 0.061107278 0.935290277 0.005277473 0.171573117 0.823149443
[34699] 0.025844317 0.198609233 0.775546432 0.007853419 0.245798156 0.746348381
[34705] 0.010039429 0.362852097 0.627108455 0.013761263 0.359638125 0.626600623
[34711] 0.018492330 0.230956212 0.750551462 0.095963463 0.426253617 0.477782875
[34717] 0.066283911 0.863279283 0.070436843 0.064778879 0.279647380 0.655573726
[34723] 0.116371177 0.595801413 0.287827432 0.021238070 0.182847947 0.795913994
[34729] 0.012580259 0.379419208 0.608000576 0.011905305 0.294728458 0.693366230
[34735] 0.008301860 0.174883932 0.816814184 0.015801996 0.173747376 0.810450613
[34741] 0.104008079 0.774980426 0.121011488 0.132294804 0.434408098 0.433297127
[34747] 0.072824761 0.534018815 0.393156409 0.061173543 0.774484932 0.164341524
[34753] 0.006506269 0.067760430 0.925733268 0.005014389 0.052598082 0.942387521
[34759] 0.019876353 0.242208689 0.737914979 0.072712444 0.494367570 0.432919979
[34765] 0.071123399 0.630852580 0.298024058 0.006869464 0.083687797 0.909442723
[34771] 0.006543685 0.112126283 0.881330073 0.009967533 0.191485256 0.798547208
[34777] 0.018305149 0.479592234 0.502102613 0.016113235 0.328066051 0.655820668
[34783] 0.016338767 0.300147086 0.683514178 0.108018249 0.826075613 0.065906070
[34789] 0.171291694 0.789665282 0.039043017 0.206422687 0.706573129 0.087004185
[34795] 0.010520880 0.397034705 0.592444420 0.094166920 0.349334687 0.556498408
[34801] 0.198907718 0.589697361 0.211394936 0.008099897 0.294399351 0.697500765
[34807] 0.040896498 0.348904371 0.610199094 0.467034429 0.404367566 0.128598005
[34813] 0.007008610 0.103572793 0.889418662 0.121905521 0.785724699 0.092369772
[34819] 0.108660534 0.751904905 0.139434561 0.070933633 0.839826584 0.089239784
[34825] 0.232288405 0.565435469 0.202276170 0.028045790 0.224443242 0.747510910
[34831] 0.131644621 0.800027668 0.068327658 0.119138129 0.610679865 0.270182014
[34837] 0.077467263 0.693654537 0.228878170 0.038319230 0.856126010 0.105554730
[34843] 0.030147659 0.322281182 0.647571206 0.011650371 0.211281791 0.777067840
[34849] 0.009091681 0.248882160 0.742026150 0.109721355 0.839606345 0.050672289
[34855] 0.415284902 0.568359911 0.016355203 0.072588012 0.643248260 0.284163684
[34861] 0.027078606 0.240846634 0.732074738 0.083222017 0.582661808 0.334116191
[34867] 0.071714349 0.530532420 0.397753239 0.155678049 0.782661915 0.061660010
[34873] 0.072283998 0.766613066 0.161102936 0.188347325 0.721633852 0.090018839
[34879] 0.012248094 0.379503876 0.608248055 0.024724429 0.753777921 0.221497700
[34885] 0.007921981 0.105741583 0.886336446 0.016340161 0.211796716 0.771863103
[34891] 0.155676514 0.675993800 0.168329641 0.173709109 0.361916006 0.464374810
[34897] 0.166031286 0.731902719 0.102066025 0.077404439 0.877858698 0.044736858
[34903] 0.036939748 0.143277287 0.819782972 0.007303442 0.079431824 0.913264751
[34909] 0.119608209 0.566436708 0.313955098 0.159486368 0.758353651 0.082159966
[34915] 0.221437246 0.727998912 0.050563790 0.011192221 0.226309881 0.762497842
[34921] 0.011329181 0.303879529 0.684791267 0.079737134 0.767612934 0.152649924
[34927] 0.003917926 0.030134309 0.965947747 0.068035021 0.304953605 0.627011359
[34933] 0.009615440 0.359761775 0.630622745 0.013623673 0.317822039 0.668554306
[34939] 0.207487211 0.753584564 0.038928233 0.096115753 0.834983408 0.068900816
[34945] 0.004395740 0.112196892 0.883407414 0.131096154 0.837572336 0.031331439
[34951] 0.020964833 0.383912086 0.595123112 0.019377446 0.264710516 0.715911984
[34957] 0.007068511 0.407091975 0.585839510 0.003382662 0.032702602 0.963914752
[34963] 0.170276105 0.786122024 0.043601904 0.154393673 0.795747995 0.049858313
[34969] 0.244891033 0.535478830 0.219630167 0.013657610 0.383943200 0.602399170
[34975] 0.176342353 0.780523479 0.043134205 0.097601824 0.833960950 0.068437181
[34981] 0.093396887 0.807189643 0.099413410 0.162428945 0.717847526 0.119723514
[34987] 0.138522089 0.829799056 0.031678863 0.004660039 0.076341391 0.918998599
[34993] 0.014451837 0.126159176 0.859389007 0.013700685 0.132975802 0.853323519
[34999] 0.013963958 0.349996835 0.636039197 0.043127075 0.614654601 0.342218339
[35005] 0.037359547 0.289685607 0.672954798 0.034857597 0.267766118 0.697376251
[35011] 0.029335758 0.303565919 0.667098343 0.012151336 0.149648622 0.838200033
[35017] 0.013413370 0.290472478 0.696114182 0.024497192 0.145745203 0.829757631
[35023] 0.032090597 0.292041928 0.675867438 0.323228747 0.618298650 0.058472607
[35029] 0.182795897 0.692659616 0.124544457 0.003699969 0.267006457 0.729293585
[35035] 0.034393858 0.619048417 0.346557736 0.014123810 0.179435462 0.806440771
[35041] 0.022521326 0.198798284 0.778680384 0.033318479 0.122409031 0.844272494
[35047] 0.009226067 0.307252347 0.683521569 0.012884397 0.086901248 0.900214374
[35053] 0.004790154 0.266992897 0.728216946 0.026904751 0.339964271 0.633131027
[35059] 0.027755937 0.317329168 0.654914916 0.005957897 0.097283147 0.896758974
[35065] 0.089317568 0.795823038 0.114859410 0.099487618 0.855493367 0.045019016
[35071] 0.048288871 0.551927388 0.399783760 0.028107990 0.201401398 0.770490646
[35077] 0.024531119 0.272557408 0.702911496 0.009035284 0.177284569 0.813680172
[35083] 0.371228516 0.517717838 0.111053683 0.185646266 0.691325426 0.123028249
[35089] 0.011266774 0.345267534 0.643465638 0.023120549 0.170996547 0.805882871
[35095] 0.144254699 0.777051747 0.078693546 0.223427609 0.755736947 0.020835454

A saída da função predict são as probabilidades de cada uma das 3 classes para cada uma das novas observações. Mas essa apresentação é bem confusa e desorganizada. Segue uma sugestão para uma saída mais amigável.

pred = predict(XGB_CLASS_3,newdata=M_X)
y_ = matrix(pred,byrow = TRUE,ncol=3,dimnames =  list(NULL,c("baixa","media","alta")))
y_

               baixa       media        alta
    [1,] 0.005048582 0.120415643 0.874535799
    [2,] 0.018599473 0.343623400 0.637777150
    [3,] 0.140126988 0.298844337 0.561028659
    [4,] 0.215170622 0.553240538 0.231588826
    [5,] 0.032674577 0.371185720 0.596139729
    [6,] 0.721569836 0.262757033 0.015673090
    [7,] 0.375060320 0.250211477 0.374728233
    [8,] 0.388041288 0.553800166 0.058158521
    [9,] 0.320265979 0.665694296 0.014039733
   [10,] 0.197767615 0.719515383 0.082716979
   [11,] 0.021728016 0.145924851 0.832347095
   [12,] 0.802626371 0.154699773 0.042673837
   [13,] 0.699973345 0.274620771 0.025405882
   [14,] 0.313374877 0.345659316 0.340965778
   [15,] 0.321086347 0.319072366 0.359841287
   [16,] 0.734190345 0.239601716 0.026207903
   [17,] 0.911634862 0.078250386 0.010114753
   [18,] 0.662990510 0.301211685 0.035797834
   [19,] 0.355923951 0.278810591 0.365265429
   [20,] 0.248273090 0.404241353 0.347485512
   [21,] 0.327105284 0.627952456 0.044942267
   [22,] 0.769827724 0.208441064 0.021731181
   [23,] 0.794421554 0.180789858 0.024788555
   [24,] 0.167649403 0.570021451 0.262329161
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 [1676,] 0.089879796 0.304053456 0.606066704
 [1677,] 0.608658910 0.375253350 0.016087769
 [1678,] 0.005767151 0.063060090 0.931172788
 [1679,] 0.027102828 0.270375431 0.702521682
 [1680,] 0.413681477 0.551949143 0.034369394
 [1681,] 0.429472536 0.527668715 0.042858727
 [1682,] 0.260941237 0.582385540 0.156673267
 [1683,] 0.031114664 0.247559547 0.721325755
 [1684,] 0.020807886 0.153787628 0.825404465
 [1685,] 0.019093225 0.296396554 0.684510171
 [1686,] 0.006899412 0.061387971 0.931712568
 [1687,] 0.019987229 0.266288310 0.713724494
 [1688,] 0.405748874 0.526245296 0.068005838
 [1689,] 0.124977924 0.790241420 0.084780686
 [1690,] 0.007783435 0.083876386 0.908340216
 [1691,] 0.034321893 0.508940935 0.456737220
 [1692,] 0.081788465 0.210023344 0.708188176
 [1693,] 0.108731225 0.533768058 0.357500762
 [1694,] 0.369188040 0.563674331 0.067137577
 [1695,] 0.006152387 0.113721237 0.880126417
 [1696,] 0.195307896 0.508670986 0.296021104
 [1697,] 0.171427563 0.765867710 0.062704705
 [1698,] 0.282555163 0.684805989 0.032638844
 [1699,] 0.434139043 0.536424458 0.029436471
 [1700,] 0.254565090 0.716893852 0.028541056
 [1701,] 0.525549531 0.393123358 0.081327103
 [1702,] 0.451801568 0.524391830 0.023806604
 [1703,] 0.471674204 0.496838421 0.031487428
 [1704,] 0.706371844 0.275577813 0.018050304
 [1705,] 0.017167311 0.223307684 0.759525001
 [1706,] 0.060782123 0.846978486 0.092239410
 [1707,] 0.122215346 0.602783382 0.275001258
 [1708,] 0.004443679 0.301308215 0.694248080
 [1709,] 0.079480335 0.717858553 0.202661097
 [1710,] 0.018675916 0.197907731 0.783416331
 [1711,] 0.017689109 0.275154710 0.707156181
 [1712,] 0.031009976 0.294371217 0.674618781
 [1713,] 0.006117423 0.053662330 0.940220177
 [1714,] 0.762194991 0.218437806 0.019367203
 [1715,] 0.455358863 0.520011663 0.024629483
 [1716,] 0.029603669 0.320056081 0.650340259
 [1717,] 0.075154558 0.514781415 0.410064012
 [1718,] 0.019678410 0.269560933 0.710760713
 [1719,] 0.019910634 0.242902637 0.737186730
 [1720,] 0.021018462 0.077919185 0.901062310
 [1721,] 0.005625254 0.049877338 0.944497466
 [1722,] 0.036787413 0.329555541 0.633657038
 [1723,] 0.008770611 0.074514762 0.916714609
 [1724,] 0.010673783 0.107057817 0.882268429
 [1725,] 0.006381728 0.059316032 0.934302211
 [1726,] 0.009456478 0.052899659 0.937643826
 [1727,] 0.148640290 0.782881141 0.068478554
 [1728,] 0.070008360 0.558749974 0.371241719
 [1729,] 0.005844504 0.056866575 0.937288880
 [1730,] 0.102408469 0.685301244 0.212290272
 [1731,] 0.600403130 0.350813985 0.048782878
 [1732,] 0.072877228 0.344867975 0.582254767
 [1733,] 0.103486985 0.542690217 0.353822798
 [1734,] 0.055392165 0.321928203 0.622679651
 [1735,] 0.094544895 0.348922372 0.556532681
 [1736,] 0.027653323 0.291619897 0.680726826
 [1737,] 0.006126903 0.081884921 0.911988199
 [1738,] 0.010890390 0.098089606 0.891020060
 [1739,] 0.029810745 0.339141756 0.631047487
 [1740,] 0.162063614 0.774833322 0.063103050
 [1741,] 0.053931750 0.574705541 0.371362686
 [1742,] 0.017272502 0.176005781 0.806721747
 [1743,] 0.005642097 0.064608783 0.929749191
 [1744,] 0.010043243 0.081388839 0.908567965
 [1745,] 0.017815316 0.109013662 0.873171031
 [1746,] 0.043606035 0.351650000 0.604743958
 [1747,] 0.127476573 0.704802871 0.167720601
 [1748,] 0.011496682 0.157971501 0.830531836
 [1749,] 0.009571889 0.155744910 0.834683239
 [1750,] 0.013927120 0.134502962 0.851569891
 [1751,] 0.027382441 0.172070205 0.800547302
 [1752,] 0.004232844 0.209059715 0.786707461
 [1753,] 0.007161489 0.063970596 0.928867936
 [1754,] 0.008642673 0.076555192 0.914802074
 [1755,] 0.021882094 0.115237154 0.862880707
 [1756,] 0.027491467 0.150813743 0.821694791
 [1757,] 0.011059072 0.087548062 0.901392877
 [1758,] 0.089231335 0.815258980 0.095509700
 [1759,] 0.044461500 0.476089329 0.479449183
 [1760,] 0.166457608 0.795747876 0.037794497
 [1761,] 0.047567125 0.458783805 0.493649125
 [1762,] 0.031787880 0.218640670 0.749571443
 [1763,] 0.118850939 0.721676171 0.159472913
 [1764,] 0.139132246 0.657914340 0.202953398
 [1765,] 0.005366823 0.317532122 0.677101076
 [1766,] 0.110965468 0.283077449 0.605957091
 [1767,] 0.003772086 0.070766099 0.925461829
 [1768,] 0.009760309 0.148209408 0.842030287
 [1769,] 0.003840953 0.102982566 0.893176496
 [1770,] 0.017179932 0.177646384 0.805173695
 [1771,] 0.026871871 0.171653420 0.801474750
 [1772,] 0.216689736 0.739393234 0.043917019
 [1773,] 0.599448323 0.369101077 0.031450611
 [1774,] 0.015651224 0.070397317 0.913951397
 [1775,] 0.023828026 0.154107198 0.822064757
 [1776,] 0.009510525 0.121661432 0.868828058
 [1777,] 0.012449351 0.192587212 0.794963479
 [1778,] 0.003654138 0.313894093 0.682451785
 [1779,] 0.048998754 0.377768755 0.573232472
 [1780,] 0.076246768 0.478147477 0.445605695
 [1781,] 0.066732958 0.503067195 0.430199802
 [1782,] 0.025929607 0.161678970 0.812391460
 [1783,] 0.011203538 0.066938981 0.921857476
 [1784,] 0.582244098 0.364577472 0.053178407
 [1785,] 0.028341709 0.271544456 0.700113833
 [1786,] 0.044887867 0.574577987 0.380534142
 [1787,] 0.092591852 0.675213277 0.232194856
 [1788,] 0.150376529 0.770173073 0.079450428
 [1789,] 0.210494980 0.582662582 0.206842437
 [1790,] 0.099432252 0.503561258 0.397006482
 [1791,] 0.125760317 0.504421353 0.369818330
 [1792,] 0.036045294 0.505552649 0.458402067
 [1793,] 0.017542390 0.043755773 0.938701868
 [1794,] 0.055138007 0.559707463 0.385154516
 [1795,] 0.305141747 0.666870534 0.027987702
 [1796,] 0.005931167 0.054323673 0.939745188
 [1797,] 0.665902257 0.124490544 0.209607199
 [1798,] 0.006869483 0.060148269 0.932982266
 [1799,] 0.005641119 0.088396288 0.905962527
 [1800,] 0.051889587 0.307005018 0.641105413
 [1801,] 0.004229462 0.037240110 0.958530426
 [1802,] 0.365860581 0.488666236 0.145473123
 [1803,] 0.069894090 0.722788036 0.207317814
 [1804,] 0.198927313 0.730436206 0.070636451
 [1805,] 0.187803850 0.658785462 0.153410673
 [1806,] 0.189340755 0.584445179 0.226214021
 [1807,] 0.207010910 0.750712752 0.042276323
 [1808,] 0.057629306 0.416131198 0.526239514
 [1809,] 0.014505065 0.124505900 0.860988975
 [1810,] 0.034589026 0.196351230 0.769059718
 [1811,] 0.020432353 0.285138220 0.694429398
 [1812,] 0.011563811 0.162001565 0.826434612
 [1813,] 0.004975476 0.124770693 0.870253801
 [1814,] 0.016617352 0.197918206 0.785464466
 [1815,] 0.011393275 0.124610133 0.863996625
 [1816,] 0.005357023 0.131431192 0.863211751
 [1817,] 0.041591294 0.271626264 0.686782420
 [1818,] 0.003553116 0.650039017 0.346407861
 [1819,] 0.301325381 0.675155580 0.023519093
 [1820,] 0.005413517 0.048477437 0.946109056
 [1821,] 0.008037807 0.086000994 0.905961156
 [1822,] 0.005058437 0.076933995 0.918007553
 [1823,] 0.002728095 0.103074923 0.894197047
 [1824,] 0.012422101 0.766079724 0.221498206
 [1825,] 0.025317973 0.224606425 0.750075638
 [1826,] 0.003605978 0.076735348 0.919658720
 [1827,] 0.033078771 0.186302751 0.780618489
 [1828,] 0.007695421 0.070130549 0.922174037
 [1829,] 0.005147722 0.075899571 0.918952644
 [1830,] 0.008535707 0.106384680 0.885079682
 [1831,] 0.006003321 0.034677017 0.959319711
 [1832,] 0.005596610 0.067728497 0.926674902
 [1833,] 0.008943851 0.086317271 0.904738903
 [1834,] 0.029469365 0.339568913 0.630961716
 [1835,] 0.004915264 0.070390463 0.924694240
 [1836,] 0.043123890 0.289353102 0.667523026
 [1837,] 0.032693677 0.379014254 0.588292062
 [1838,] 0.208130136 0.605768263 0.186101601
 [1839,] 0.574737251 0.399259865 0.026002897
 [1840,] 0.013454357 0.193584844 0.792960823
 [1841,] 0.006112917 0.074716955 0.919170141
 [1842,] 0.005210694 0.087482013 0.907307267
 [1843,] 0.014778021 0.165157512 0.820064485
 [1844,] 0.015743792 0.140182436 0.844073772
 [1845,] 0.006249683 0.151944995 0.841805339
 [1846,] 0.028966432 0.406868339 0.564165235
 [1847,] 0.011791182 0.083623983 0.904584885
 [1848,] 0.049547903 0.492534906 0.457917184
 [1849,] 0.279029727 0.577974558 0.142995730
 [1850,] 0.057902806 0.232006177 0.710091054
 [1851,] 0.445737243 0.493125826 0.061136954
 [1852,] 0.059210412 0.254922032 0.685867548
 [1853,] 0.205062091 0.713139296 0.081798606
 [1854,] 0.219901398 0.682944417 0.097154118
 [1855,] 0.054832108 0.540496945 0.404670954
 [1856,] 0.062219076 0.430378258 0.507402658
 [1857,] 0.005142325 0.044485055 0.950372577
 [1858,] 0.238562480 0.728512228 0.032925297
 [1859,] 0.177647620 0.717460573 0.104891829
 [1860,] 0.003690185 0.031915717 0.964394152
 [1861,] 0.133901536 0.400093198 0.466005236
 [1862,] 0.198418409 0.728591740 0.072989866
 [1863,] 0.008101020 0.111552283 0.880346715
 [1864,] 0.016017411 0.105266899 0.878715634
 [1865,] 0.110961564 0.615437686 0.273600787
 [1866,] 0.006646120 0.048470985 0.944882870
 [1867,] 0.005154769 0.051742692 0.943102598
 [1868,] 0.007646106 0.069483727 0.922870100
 [1869,] 0.004449073 0.046699427 0.948851466
 [1870,] 0.011493372 0.086127609 0.902378976
 [1871,] 0.018527437 0.094690271 0.886782348
 [1872,] 0.007674900 0.083972111 0.908352971
 [1873,] 0.006051415 0.051127896 0.942820609
 [1874,] 0.028988397 0.237036914 0.733974636
 [1875,] 0.010694462 0.063536040 0.925769567
 [1876,] 0.090865411 0.611453056 0.297681540
 [1877,] 0.010571396 0.072354391 0.917074203
 [1878,] 0.785175622 0.203930408 0.010893969
 [1879,] 0.816690028 0.174432769 0.008877239
 [1880,] 0.019323915 0.210358351 0.770317674
 [1881,] 0.916658700 0.076758943 0.006582323
 [1882,] 0.918768466 0.074564189 0.006667286
 [1883,] 0.578575253 0.359396338 0.062028449
 [1884,] 0.457356662 0.375005215 0.167638123
 [1885,] 0.015054412 0.160124972 0.824820638
 [1886,] 0.021661283 0.189302415 0.789036334
 [1887,] 0.812765002 0.176226661 0.011008335
 [1888,] 0.008428824 0.560364604 0.431206584
 [1889,] 0.688432813 0.294822633 0.016744558
 [1890,] 0.869402826 0.121813804 0.008783408
 [1891,] 0.547948599 0.420328140 0.031723265
 [1892,] 0.649145782 0.327128112 0.023726095
 [1893,] 0.730272353 0.261895508 0.007832116
 [1894,] 0.754911125 0.231994003 0.013094857
 [1895,] 0.008410793 0.096685842 0.894903421
 [1896,] 0.036068887 0.244167551 0.719763517
 [1897,] 0.013304818 0.192650005 0.794045210
 [1898,] 0.058392782 0.350605339 0.591001868
 [1899,] 0.033982303 0.261321366 0.704696357
 [1900,] 0.626460612 0.353652716 0.019886721
 [1901,] 0.026304860 0.297690272 0.676004887
 [1902,] 0.640760422 0.338671237 0.020568360
 [1903,] 0.568512976 0.305300325 0.126186684
 [1904,] 0.003893433 0.362607211 0.633499324
 [1905,] 0.474893779 0.470597655 0.054508571
 [1906,] 0.744255364 0.229660690 0.026083944
 [1907,] 0.519861758 0.469743758 0.010394459
 [1908,] 0.775764883 0.214877456 0.009357622
 [1909,] 0.022890273 0.141776994 0.835332751
 [1910,] 0.063775778 0.226022959 0.710201263
 [1911,] 0.739215612 0.250086933 0.010697465
 [1912,] 0.796826839 0.190021783 0.013151386
 [1913,] 0.632796824 0.345205873 0.021997277
 [1914,] 0.492955267 0.475001067 0.032043677
 [1915,] 0.704239905 0.274949312 0.020810751
 [1916,] 0.596457005 0.392644078 0.010898979
 [1917,] 0.668104291 0.310276419 0.021619251
 [1918,] 0.735049248 0.252034098 0.012916587
 [1919,] 0.479143232 0.489267737 0.031588972
 [1920,] 0.741419435 0.242098376 0.016482148
 [1921,] 0.034545567 0.211647242 0.753807127
 [1922,] 0.795516729 0.195478559 0.009004676
 [1923,] 0.491160572 0.388139099 0.120700300
 [1924,] 0.560047865 0.415833384 0.024118757
 [1925,] 0.543849289 0.439330876 0.016819838
 [1926,] 0.773535371 0.200824752 0.025639897
 [1927,] 0.756557047 0.225224152 0.018218793
 [1928,] 0.359327883 0.629226983 0.011445127
 [1929,] 0.764613509 0.224061877 0.011324604
 [1930,] 0.638082623 0.296237051 0.065680310
 [1931,] 0.843134046 0.142375648 0.014490282
 [1932,] 0.490246028 0.494266212 0.015487761
 [1933,] 0.450122923 0.435264617 0.114612430
 [1934,] 0.707493484 0.280202091 0.012304457
 [1935,] 0.476815194 0.430378318 0.092806429
 [1936,] 0.816633105 0.168684304 0.014682597
 [1937,] 0.915298283 0.076750346 0.007951410
 [1938,] 0.751779139 0.239112318 0.009108564
 [1939,] 0.614379346 0.364192843 0.021427749
 [1940,] 0.742399216 0.245948091 0.011652633
 [1941,] 0.016327281 0.207375184 0.776297569
 [1942,] 0.021048442 0.221476838 0.757474780
 [1943,] 0.914729774 0.079146877 0.006123400
 [1944,] 0.706692934 0.274999470 0.018307604
 [1945,] 0.476119459 0.473771006 0.050109584
 [1946,] 0.278666079 0.411652803 0.309681088
 [1947,] 0.452266902 0.523552477 0.024180647
 [1948,] 0.279566914 0.454720736 0.265712380
 [1949,] 0.786238194 0.203198299 0.010563537
 [1950,] 0.785673380 0.204992861 0.009333804
 [1951,] 0.043110684 0.349702746 0.607186556
 [1952,] 0.015176826 0.174941689 0.809881449
 [1953,] 0.396355063 0.578884661 0.024760323
 [1954,] 0.757258177 0.222162127 0.020579711
 [1955,] 0.034167174 0.198838770 0.766994059
 [1956,] 0.727568269 0.261654437 0.010777324
 [1957,] 0.579686403 0.377855152 0.042458404
 [1958,] 0.628940105 0.338570297 0.032489639
 [1959,] 0.666753471 0.169347197 0.163899347
 [1960,] 0.638925195 0.338113219 0.022961572
 [1961,] 0.417439491 0.427371740 0.155188754
 [1962,] 0.659024596 0.320666015 0.020309392
 [1963,] 0.765207529 0.219826102 0.014966404
 [1964,] 0.720627308 0.262755573 0.016617065
 [1965,] 0.847891927 0.145435914 0.006672166
 [1966,] 0.027522678 0.307074457 0.665402830
 [1967,] 0.662348688 0.326203376 0.011447949
 [1968,] 0.836140394 0.156828105 0.007031469
 [1969,] 0.538005888 0.321671575 0.140322581
 [1970,] 0.838231683 0.154396981 0.007371277
 [1971,] 0.052011117 0.264199734 0.683789194
 [1972,] 0.688197553 0.296660721 0.015141764
 [1973,] 0.740871847 0.249643654 0.009484556
 [1974,] 0.882892609 0.110306434 0.006800923
 [1975,] 0.399558216 0.398775131 0.201666698
 [1976,] 0.779253066 0.203735545 0.017011367
 [1977,] 0.621287644 0.355895370 0.022816988
 [1978,] 0.033901572 0.278536499 0.687561929
 [1979,] 0.756666183 0.222137094 0.021196723
 [1980,] 0.067393690 0.236355364 0.696250975
 [1981,] 0.668275654 0.296292692 0.035431702
 [1982,] 0.763251543 0.217256695 0.019491751
 [1983,] 0.547466815 0.392104119 0.060429074
 [1984,] 0.766812742 0.227194339 0.005992859
 [1985,] 0.014128095 0.133162886 0.852709055
 [1986,] 0.017718475 0.122137249 0.860144317
 [1987,] 0.495884478 0.434103668 0.070011906
 [1988,] 0.026074817 0.173192292 0.800732851
 [1989,] 0.015249687 0.142643139 0.842107117
 [1990,] 0.018820025 0.149592817 0.831587136
 [1991,] 0.008110508 0.230402708 0.761486828
 [1992,] 0.005154565 0.031336520 0.963508904
 [1993,] 0.513202667 0.460324436 0.026472850
 [1994,] 0.644204557 0.342302352 0.013493137
 [1995,] 0.865692139 0.126508161 0.007799707
 [1996,] 0.534279943 0.399539530 0.066180512
 [1997,] 0.875273407 0.117123127 0.007603510
 [1998,] 0.635853291 0.343002677 0.021143980
 [1999,] 0.779055178 0.207857475 0.013087350
 [2000,] 0.123500809 0.683010638 0.193488523
 [2001,] 0.602736592 0.364685148 0.032578241
 [2002,] 0.761447549 0.224536523 0.014015898
 [2003,] 0.610204816 0.369421422 0.020373804
 [2004,] 0.293992996 0.565822542 0.140184447
 [2005,] 0.016952928 0.199558556 0.783488512
 [2006,] 0.022153519 0.174837351 0.803009093
 [2007,] 0.011622559 0.097126655 0.891250730
 [2008,] 0.014641381 0.158196986 0.827161610
 [2009,] 0.023618363 0.265562773 0.710818887
 [2010,] 0.034685679 0.230971992 0.734342337
 [2011,] 0.040000193 0.323807806 0.636191964
 [2012,] 0.715689600 0.239441976 0.044868387
 [2013,] 0.606735706 0.377205908 0.016058423
 [2014,] 0.780798733 0.206965610 0.012235682
 [2015,] 0.871633947 0.119783163 0.008582898
 [2016,] 0.032692455 0.196518987 0.770788550
 [2017,] 0.024756603 0.225405917 0.749837458
 [2018,] 0.601811707 0.383851737 0.014336609
 [2019,] 0.565779567 0.400372803 0.033847671
 [2020,] 0.722512245 0.264903098 0.012584600
 [2021,] 0.027526822 0.200045735 0.772427499
 [2022,] 0.018195512 0.100185774 0.881618679
 [2023,] 0.015298801 0.237304911 0.747396290
 [2024,] 0.004293004 0.632853210 0.362853795
 [2025,] 0.026517430 0.180477098 0.793005466
 [2026,] 0.020263406 0.405370742 0.574365854
 [2027,] 0.596040666 0.393430173 0.010529168
 [2028,] 0.047141444 0.313693672 0.639164865
 [2029,] 0.642059565 0.334972501 0.022967899
 [2030,] 0.027126810 0.212690070 0.760183156
 [2031,] 0.847879291 0.144459218 0.007661528
 [2032,] 0.793577015 0.196584687 0.009838293
 [2033,] 0.029413564 0.296588689 0.673997700
 [2034,] 0.059270330 0.377294421 0.563435256
 [2035,] 0.013916828 0.152750060 0.833333135
 [2036,] 0.007286211 0.414905697 0.577808082
 [2037,] 0.067110740 0.373822123 0.559067130
 [2038,] 0.420772314 0.367859840 0.211367846
 [2039,] 0.018415965 0.193697318 0.787886739
 [2040,] 0.042929512 0.399427593 0.557642937
 [2041,] 0.039093379 0.225473195 0.735433400
 [2042,] 0.026263986 0.225454241 0.748281837
 [2043,] 0.014696887 0.159552291 0.825750828
 [2044,] 0.012606154 0.143315196 0.844078660
 [2045,] 0.850401521 0.141378462 0.008220076
 [2046,] 0.436048716 0.502910614 0.061040651
 [2047,] 0.069192283 0.459333986 0.471473753
 [2048,] 0.046897072 0.343088806 0.610014141
 [2049,] 0.007768104 0.347899526 0.644332409
 [2050,] 0.005413617 0.279043734 0.715542674
 [2051,] 0.029920474 0.197181180 0.772898316
 [2052,] 0.014068432 0.135238037 0.850693524
 [2053,] 0.023895752 0.191587612 0.784516633
 [2054,] 0.066869512 0.340825886 0.592304647
 [2055,] 0.039314460 0.307911634 0.652773917
 [2056,] 0.028732385 0.418764204 0.552503407
 [2057,] 0.023655392 0.522998691 0.453345925
 [2058,] 0.026005153 0.121296898 0.852697968
 [2059,] 0.012577527 0.141712084 0.845710397
 [2060,] 0.020398112 0.142782226 0.836819649
 [2061,] 0.023987480 0.123421595 0.852590919
 [2062,] 0.024335628 0.190741643 0.784922719
 [2063,] 0.092482664 0.391070843 0.516446471
 [2064,] 0.041855607 0.199439362 0.758704960
 [2065,] 0.033379082 0.238354906 0.728266001
 [2066,] 0.026799016 0.115742050 0.857458889
 [2067,] 0.055848781 0.366826177 0.577325046
 [2068,] 0.006114439 0.085228987 0.908656538
 [2069,] 0.021275114 0.163875833 0.814849079
 [2070,] 0.004758708 0.050544880 0.944696367
 [2071,] 0.014868161 0.179035291 0.806096494
 [2072,] 0.025005508 0.191804469 0.783190012
 [2073,] 0.031301953 0.245824128 0.722873867
 [2074,] 0.064958587 0.401757300 0.533284128
 [2075,] 0.040916923 0.265909135 0.693173945
 [2076,] 0.130209044 0.291759610 0.578031301
 [2077,] 0.055871256 0.345581621 0.598547101
 [2078,] 0.479925662 0.503703654 0.016370660
 [2079,] 0.573003352 0.408669382 0.018327251
 [2080,] 0.675863564 0.301992714 0.022143705
 [2081,] 0.165161222 0.464772373 0.370066404
 [2082,] 0.079017885 0.352860719 0.568121374
 [2083,] 0.025739770 0.193705559 0.780554712
 [2084,] 0.712014675 0.263220429 0.024764923
 [2085,] 0.820601702 0.167016566 0.012381749
 [2086,] 0.662088156 0.253874600 0.084037259
 [2087,] 0.537399471 0.435645550 0.026954997
 [2088,] 0.579393387 0.396667302 0.023939315
 [2089,] 0.673624754 0.286539972 0.039835304
 [2090,] 0.591753900 0.389224708 0.019021407
 [2091,] 0.632930219 0.333845168 0.033224642
 [2092,] 0.269323111 0.587252438 0.143424422
 [2093,] 0.629415333 0.350728035 0.019856682
 [2094,] 0.855426669 0.125500575 0.019072773
 [2095,] 0.025687719 0.194852501 0.779459834
 [2096,] 0.038675532 0.242045045 0.719279468
 [2097,] 0.658689141 0.328302860 0.013007967
 [2098,] 0.455415040 0.520251989 0.024332961
 [2099,] 0.536937118 0.438399345 0.024663551
 [2100,] 0.032203611 0.156262815 0.811533570
 [2101,] 0.639331043 0.337643266 0.023025740
 [2102,] 0.325144738 0.529747963 0.145107239
 [2103,] 0.637473583 0.345387042 0.017139396
 [2104,] 0.711935520 0.269468606 0.018595882
 [2105,] 0.796800315 0.173279345 0.029920327
 [2106,] 0.441127330 0.412854671 0.146017984
 [2107,] 0.394972861 0.484478354 0.120548740
 [2108,] 0.481511325 0.462188989 0.056299675
 [2109,] 0.402142346 0.486046314 0.111811303
 [2110,] 0.629899085 0.327415645 0.042685285
 [2111,] 0.447334617 0.493495822 0.059169568
 [2112,] 0.386646360 0.367542833 0.245810807
 [2113,] 0.401256233 0.528996408 0.069747359
 [2114,] 0.630999506 0.324175358 0.044825159
 [2115,] 0.017187091 0.080402911 0.902409971
 [2116,] 0.513653338 0.429727286 0.056619372
 [2117,] 0.662222207 0.288829952 0.048947848
 [2118,] 0.249279946 0.640959322 0.109760746
 [2119,] 0.423471421 0.465750754 0.110777788
 [2120,] 0.485492200 0.452328205 0.062179603
 [2121,] 0.046322197 0.188337088 0.765340745
 [2122,] 0.484723240 0.429325193 0.085951552
 [2123,] 0.660884678 0.258121759 0.080993555
 [2124,] 0.721711695 0.234820098 0.043468252
 [2125,] 0.007747868 0.108964086 0.883288085
 [2126,] 0.110889949 0.523584306 0.365525723
 [2127,] 0.014732349 0.185478225 0.799789429
 [2128,] 0.701239526 0.275274158 0.023486309
 [2129,] 0.017137555 0.071638465 0.911224008
 [2130,] 0.609228492 0.356112272 0.034659255
 [2131,] 0.576027751 0.371748418 0.052223820
 [2132,] 0.765615880 0.194729313 0.039654847
 [2133,] 0.518500984 0.424085915 0.057413083
 [2134,] 0.569537222 0.261710405 0.168752328
 [2135,] 0.057756521 0.189097524 0.753145933
 [2136,] 0.445977867 0.392330617 0.161691517
 [2137,] 0.847790778 0.134553418 0.017655833
 [2138,] 0.696420372 0.250205636 0.053374019
 [2139,] 0.426840514 0.351675928 0.221483588
 [2140,] 0.594252646 0.382054508 0.023692859
 [2141,] 0.547247946 0.414681166 0.038070906
 [2142,] 0.632877052 0.290302426 0.076820493
 [2143,] 0.737304330 0.226350293 0.036345351
 [2144,] 0.663720608 0.284545511 0.051733896
 [2145,] 0.664091825 0.290506452 0.045401722
 [2146,] 0.687820196 0.294881463 0.017298343
 [2147,] 0.754318058 0.225985005 0.019696929
 [2148,] 0.432967037 0.416298866 0.150734112
 [2149,] 0.180487111 0.714512110 0.105000734
 [2150,] 0.750535667 0.230126724 0.019337619
 [2151,] 0.722071528 0.260273367 0.017655099
 [2152,] 0.646238565 0.299726039 0.054035407
 [2153,] 0.572147071 0.395651698 0.032201234
 [2154,] 0.626534045 0.337217808 0.036248144
 [2155,] 0.657755852 0.294704974 0.047539171
 [2156,] 0.179043978 0.272323638 0.548632383
 [2157,] 0.579173386 0.392177403 0.028649200
 [2158,] 0.024017947 0.170556203 0.805425882
 [2159,] 0.671727300 0.288141489 0.040131234
 [2160,] 0.472375661 0.480974823 0.046649523
 [2161,] 0.597036839 0.351568013 0.051395103
 [2162,] 0.343136907 0.618728817 0.038134266
 [2163,] 0.020779571 0.116780609 0.862439811
 [2164,] 0.614313960 0.255642295 0.130043820
 [2165,] 0.047415141 0.411864072 0.540720761
 [2166,] 0.410157621 0.537989855 0.051852539
 [2167,] 0.648252487 0.299235493 0.052512020
 [2168,] 0.638610184 0.252189875 0.109199911
 [2169,] 0.309840858 0.582443714 0.107715458
 [2170,] 0.511586547 0.407376587 0.081036858
 [2171,] 0.592353642 0.317122996 0.090523355
 [2172,] 0.639412761 0.316843390 0.043743875
 [2173,] 0.590012074 0.332130492 0.077857383
 [2174,] 0.459359676 0.460976064 0.079664297
 [2175,] 0.530519962 0.439439535 0.030040532
 [2176,] 0.524070442 0.338746578 0.137183025
 [2177,] 0.349441677 0.429253161 0.221305117
 [2178,] 0.678456724 0.280039847 0.041503396
 [2179,] 0.734905779 0.237236783 0.027857451
 [2180,] 0.629588962 0.188750580 0.181660414
 [2181,] 0.439627081 0.500475168 0.059897788
 [2182,] 0.455642819 0.511536956 0.032820258
 [2183,] 0.729614735 0.233200312 0.037184939
 [2184,] 0.858221173 0.117366828 0.024411993
 [2185,] 0.720389068 0.223106474 0.056504469
 [2186,] 0.720128894 0.264383554 0.015487519
 [2187,] 0.689076245 0.283515483 0.027408257
 [2188,] 0.804307997 0.161584020 0.034107979
 [2189,] 0.669229627 0.316236943 0.014533403
 [2190,] 0.520237684 0.359076142 0.120686226
 [2191,] 0.638655961 0.345990270 0.015353747
 [2192,] 0.252372712 0.694757521 0.052869763
 [2193,] 0.514393628 0.459593147 0.026013223
 [2194,] 0.410786062 0.546840727 0.042373259
 [2195,] 0.511392415 0.452405542 0.036202017
 [2196,] 0.011868545 0.104623221 0.883508265
 [2197,] 0.533711016 0.396983713 0.069305263
 [2198,] 0.017718436 0.140340149 0.841941357
 [2199,] 0.401352644 0.569193721 0.029453611
 [2200,] 0.466873318 0.450632066 0.082494654
 [2201,] 0.161484823 0.476422369 0.362092763
 [2202,] 0.452013195 0.527375877 0.020610936
 [2203,] 0.605209291 0.346542150 0.048248567
 [2204,] 0.691061556 0.263548523 0.045389935
 [2205,] 0.685544074 0.283641189 0.030814683
 [2206,] 0.586051345 0.373055935 0.040892694
 [2207,] 0.701922238 0.257955134 0.040122684
 [2208,] 0.864619255 0.125895664 0.009485024
 [2209,] 0.612839699 0.342625320 0.044534955
 [2210,] 0.014395761 0.113725655 0.871878564
 [2211,] 0.566687286 0.411229819 0.022082899
 [2212,] 0.427445054 0.553888917 0.018666066
 [2213,] 0.784142852 0.192353711 0.023503419
 [2214,] 0.490695536 0.342711717 0.166592732
 [2215,] 0.076197252 0.245451659 0.678351104
 [2216,] 0.008411071 0.077704079 0.913884819
 [2217,] 0.023444997 0.158764869 0.817790091
 [2218,] 0.047150888 0.261062771 0.691786349
 [2219,] 0.621476352 0.352000266 0.026523354
 [2220,] 0.256632358 0.681803167 0.061564524
 [2221,] 0.509850621 0.475352943 0.014796478
 [2222,] 0.366754383 0.575465381 0.057780214
 [2223,] 0.336270362 0.633216560 0.030513091
 [2224,] 0.322934121 0.401256531 0.275809348
 [2225,] 0.253503948 0.413575172 0.332920879
 [2226,] 0.746637344 0.235491410 0.017871203
 [2227,] 0.319323331 0.655508578 0.025168106
 [2228,] 0.363223881 0.565280080 0.071496010
 [2229,] 0.467157394 0.502584696 0.030257935
 [2230,] 0.239799500 0.489992499 0.270208031
 [2231,] 0.725357413 0.251444161 0.023198456
 [2232,] 0.014130989 0.119454324 0.866414666
 [2233,] 0.545257330 0.409157455 0.045585182
 [2234,] 0.311193079 0.651361585 0.037445344
 [2235,] 0.611164272 0.368133992 0.020701760
 [2236,] 0.602391899 0.365173250 0.032434881
 [2237,] 0.435702413 0.510456622 0.053841025
 [2238,] 0.003851038 0.078061976 0.918087006
 [2239,] 0.637716234 0.321788222 0.040495522
 [2240,] 0.597132325 0.341429353 0.061438311
 [2241,] 0.017605627 0.234867737 0.747526646
 [2242,] 0.062007613 0.305013925 0.632978499
 [2243,] 0.612814069 0.351291716 0.035894286
 [2244,] 0.462173700 0.454490423 0.083335862
 [2245,] 0.591293395 0.391837567 0.016869044
 [2246,] 0.809449375 0.173868448 0.016682217
 [2247,] 0.562514424 0.412324756 0.025160810
 [2248,] 0.844033182 0.138071716 0.017895106
 [2249,] 0.775691032 0.207801655 0.016507341
 [2250,] 0.022139648 0.145777822 0.832082570
 [2251,] 0.842316329 0.144696951 0.012986751
 [2252,] 0.685188711 0.273370057 0.041441210
 [2253,] 0.568614185 0.386402339 0.044983447
 [2254,] 0.414363086 0.479055732 0.106581129
 [2255,] 0.628712475 0.328695327 0.042592205
 [2256,] 0.632571220 0.341644883 0.025783883
 [2257,] 0.023034154 0.236144945 0.740820944
 [2258,] 0.019997442 0.174387991 0.805614531
 [2259,] 0.652307332 0.319986850 0.027705815
 [2260,] 0.900256038 0.089512646 0.010231323
 [2261,] 0.421438038 0.460550904 0.118011065
 [2262,] 0.093685851 0.364023089 0.542291105
 [2263,] 0.087251253 0.416723281 0.496025473
 [2264,] 0.527771175 0.451598108 0.020630706
 [2265,] 0.621751308 0.358229250 0.020019433
 [2266,] 0.017015781 0.171850592 0.811133683
 [2267,] 0.283792973 0.266688675 0.449518263
 [2268,] 0.018712828 0.120110378 0.861176848
 [2269,] 0.007033353 0.107334957 0.885631740
 [2270,] 0.004181688 0.049966048 0.945852280
 [2271,] 0.020637598 0.156825989 0.822536409
 [2272,] 0.011116886 0.122372225 0.866510928
 [2273,] 0.014876870 0.068364523 0.916758597
 [2274,] 0.337005824 0.549254596 0.113739572
 [2275,] 0.514105320 0.466944247 0.018950462
 [2276,] 0.066884883 0.726458013 0.206657127
 [2277,] 0.787110507 0.184450373 0.028439175
 [2278,] 0.472256601 0.509228528 0.018514853
 [2279,] 0.540070772 0.430287838 0.029641354
 [2280,] 0.488015682 0.419622660 0.092361674
 [2281,] 0.070084296 0.156731308 0.773184359
 [2282,] 0.556495547 0.410183072 0.033321347
 [2283,] 0.417893738 0.554609239 0.027497031
 [2284,] 0.542362928 0.423350304 0.034286775
 [2285,] 0.386658758 0.580273092 0.033068150
 [2286,] 0.485171080 0.441597760 0.073231153
 [2287,] 0.515779853 0.430994958 0.053225253
 [2288,] 0.100804426 0.798503757 0.100691743
 [2289,] 0.482858598 0.503047347 0.014094096
 [2290,] 0.009809545 0.429378629 0.560811877
 [2291,] 0.037204459 0.424696416 0.538099110
 [2292,] 0.003050657 0.041558780 0.955390573
 [2293,] 0.002021384 0.127736166 0.870242417
 [2294,] 0.009927512 0.085840113 0.904232383
 [2295,] 0.012492569 0.139749140 0.847758293
 [2296,] 0.007340993 0.090177491 0.902481496
 [2297,] 0.008141491 0.107746035 0.884112537
 [2298,] 0.123887904 0.207766384 0.668345749
 [2299,] 0.046343852 0.277400523 0.676255643
 [2300,] 0.052025136 0.502633631 0.445341229
 [2301,] 0.025990494 0.230585009 0.743424475
 [2302,] 0.013912850 0.124818429 0.861268699
 [2303,] 0.009634398 0.720596910 0.269768625
 [2304,] 0.648572206 0.281927884 0.069499947
 [2305,] 0.007216946 0.024862265 0.967920721
 [2306,] 0.648472965 0.328088850 0.023438172
 [2307,] 0.035654601 0.199761391 0.764584064
 [2308,] 0.013179041 0.139368385 0.847452641
 [2309,] 0.133587837 0.475519449 0.390892744
 [2310,] 0.047038920 0.290094346 0.662866771
 [2311,] 0.009404801 0.109627485 0.880967736
 [2312,] 0.013128430 0.136036515 0.850835025
 [2313,] 0.023457967 0.146516323 0.830025733
 [2314,] 0.052860197 0.256519794 0.690620065
 [2315,] 0.305123955 0.470841110 0.224034935
 [2316,] 0.310606688 0.582793713 0.106599621
 [2317,] 0.007615601 0.706195414 0.286188990
 [2318,] 0.041616898 0.305016875 0.653366268
 [2319,] 0.028742636 0.254277766 0.716979563
 [2320,] 0.019476639 0.123467796 0.857055604
 [2321,] 0.063655175 0.440184981 0.496159822
 [2322,] 0.006078936 0.055229306 0.938691795
 [2323,] 0.007335769 0.081248328 0.911415875
 [2324,] 0.578629076 0.403739929 0.017630953
 [2325,] 0.097005844 0.416224241 0.486769974
 [2326,] 0.020396490 0.206684649 0.772918940
 [2327,] 0.559225857 0.403030008 0.037744127
 [2328,] 0.621411324 0.341270059 0.037318639
 [2329,] 0.024925672 0.237509683 0.737564623
 [2330,] 0.027595339 0.119751438 0.852653205
 [2331,] 0.457176298 0.504823565 0.038000148
 [2332,] 0.053914331 0.303649962 0.642435670
 [2333,] 0.776533484 0.203166708 0.020299772
 [2334,] 0.018198606 0.140081048 0.841720402
 [2335,] 0.017733457 0.166875631 0.815390885
 [2336,] 0.045745455 0.425727963 0.528526604
 [2337,] 0.766132832 0.193212688 0.040654484
 [2338,] 0.009495518 0.091611549 0.898892939
 [2339,] 0.002376112 0.030712649 0.966911256
 [2340,] 0.020904256 0.150217548 0.828878224
 [2341,] 0.061872952 0.419597268 0.518529773
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[11630,] 0.016340161 0.211796716 0.771863103
[11631,] 0.155676514 0.675993800 0.168329641
[11632,] 0.173709109 0.361916006 0.464374810
[11633,] 0.166031286 0.731902719 0.102066025
[11634,] 0.077404439 0.877858698 0.044736858
[11635,] 0.036939748 0.143277287 0.819782972
[11636,] 0.007303442 0.079431824 0.913264751
[11637,] 0.119608209 0.566436708 0.313955098
[11638,] 0.159486368 0.758353651 0.082159966
[11639,] 0.221437246 0.727998912 0.050563790
[11640,] 0.011192221 0.226309881 0.762497842
[11641,] 0.011329181 0.303879529 0.684791267
[11642,] 0.079737134 0.767612934 0.152649924
[11643,] 0.003917926 0.030134309 0.965947747
[11644,] 0.068035021 0.304953605 0.627011359
[11645,] 0.009615440 0.359761775 0.630622745
[11646,] 0.013623673 0.317822039 0.668554306
[11647,] 0.207487211 0.753584564 0.038928233
[11648,] 0.096115753 0.834983408 0.068900816
[11649,] 0.004395740 0.112196892 0.883407414
[11650,] 0.131096154 0.837572336 0.031331439
[11651,] 0.020964833 0.383912086 0.595123112
[11652,] 0.019377446 0.264710516 0.715911984
[11653,] 0.007068511 0.407091975 0.585839510
[11654,] 0.003382662 0.032702602 0.963914752
[11655,] 0.170276105 0.786122024 0.043601904
[11656,] 0.154393673 0.795747995 0.049858313
[11657,] 0.244891033 0.535478830 0.219630167
[11658,] 0.013657610 0.383943200 0.602399170
[11659,] 0.176342353 0.780523479 0.043134205
[11660,] 0.097601824 0.833960950 0.068437181
[11661,] 0.093396887 0.807189643 0.099413410
[11662,] 0.162428945 0.717847526 0.119723514
[11663,] 0.138522089 0.829799056 0.031678863
[11664,] 0.004660039 0.076341391 0.918998599
[11665,] 0.014451837 0.126159176 0.859389007
[11666,] 0.013700685 0.132975802 0.853323519
[11667,] 0.013963958 0.349996835 0.636039197
[11668,] 0.043127075 0.614654601 0.342218339
[11669,] 0.037359547 0.289685607 0.672954798
[11670,] 0.034857597 0.267766118 0.697376251
[11671,] 0.029335758 0.303565919 0.667098343
[11672,] 0.012151336 0.149648622 0.838200033
[11673,] 0.013413370 0.290472478 0.696114182
[11674,] 0.024497192 0.145745203 0.829757631
[11675,] 0.032090597 0.292041928 0.675867438
[11676,] 0.323228747 0.618298650 0.058472607
[11677,] 0.182795897 0.692659616 0.124544457
[11678,] 0.003699969 0.267006457 0.729293585
[11679,] 0.034393858 0.619048417 0.346557736
[11680,] 0.014123810 0.179435462 0.806440771
[11681,] 0.022521326 0.198798284 0.778680384
[11682,] 0.033318479 0.122409031 0.844272494
[11683,] 0.009226067 0.307252347 0.683521569
[11684,] 0.012884397 0.086901248 0.900214374
[11685,] 0.004790154 0.266992897 0.728216946
[11686,] 0.026904751 0.339964271 0.633131027
[11687,] 0.027755937 0.317329168 0.654914916
[11688,] 0.005957897 0.097283147 0.896758974
[11689,] 0.089317568 0.795823038 0.114859410
[11690,] 0.099487618 0.855493367 0.045019016
[11691,] 0.048288871 0.551927388 0.399783760
[11692,] 0.028107990 0.201401398 0.770490646
[11693,] 0.024531119 0.272557408 0.702911496
[11694,] 0.009035284 0.177284569 0.813680172
[11695,] 0.371228516 0.517717838 0.111053683
[11696,] 0.185646266 0.691325426 0.123028249
[11697,] 0.011266774 0.345267534 0.643465638
[11698,] 0.023120549 0.170996547 0.805882871
[11699,] 0.144254699 0.777051747 0.078693546
[11700,] 0.223427609 0.755736947 0.020835454

A classe prevista será aquela com maior probabilidade de ocorrer.

y_classe = ifelse(y_[,"alta"]>y_[,"baixa"] & y_[,"alta"]>y_[,"media"],"alta", ifelse(y_[,"baixa"]>y_[,"media"],"baixa","media"))
y_classe = factor(y_classe)
levels(y_classe)

[1] "alta"  "baixa" "media"

confusionMatrix(data = y_classe, reference = base_treino$TAXA_PART_CAT)

Confusion Matrix and Statistics

          Reference
Prediction alta baixa media
     alta  3470   145   861
     baixa  155  3488  1030
     media  356   330  1865

Overall Statistics
                                          
               Accuracy : 0.7541          
                 95% CI : (0.7462, 0.7619)
    No Information Rate : 0.3403          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.63            
                                          
 Mcnemar's Test P-Value : < 2.2e-16       

Statistics by Class:

                     Class: alta Class: baixa Class: media
Sensitivity               0.8716       0.8801       0.4965
Specificity               0.8697       0.8468       0.9136
Pos Pred Value            0.7752       0.7464       0.7311
Neg Pred Value            0.9293       0.9324       0.7933
Prevalence                0.3403       0.3387       0.3210
Detection Rate            0.2966       0.2981       0.1594
Detection Prevalence      0.3826       0.3994       0.2180
Balanced Accuracy         0.8707       0.8635       0.7051

saveRDS(XGB_REG,file="salvos//XGB_REG.rds")
saveRDS(XGB_CLASS_2,file="salvos//XGB_CLASS_2.rds")
saveRDS(XGB_CLASS_3,file="salvos//XGB_CLASS_3.rds")