Data for Titanic survival

Let’s see an example for DALEX package for classification models for the survival problem for Titanic dataset. Here we are using a dataset titanic avaliable in teh DALEX package. Note that this data was copied from the stablelearner package.

library("DALEX")
head(titanic_imputed)

#>   gender age class    embarked  fare sibsp parch survived
#> 1   male  42   3rd Southampton  7.11     0     0        0
#> 2   male  13   3rd Southampton 20.05     0     2        0
#> 3   male  16   3rd Southampton 20.05     1     1        0
#> 4 female  39   3rd Southampton 20.05     1     1        1
#> 5 female  16   3rd Southampton  7.13     0     0        1
#> 6   male  25   3rd Southampton  7.13     0     0        1

Model for Titanic survival

Ok, not it’s time to create a model. Let’s use the Random Forest model.

# prepare model
library("ranger")
model_titanic_rf <- ranger(survived ~ gender + age + class + embarked +
                                   fare + sibsp + parch,  data = titanic_imputed,
                           classification = TRUE)
model_titanic_rf

#> Ranger result
#> 
#> Call:
#>  ranger(survived ~ gender + age + class + embarked + fare + sibsp +      parch, data = titanic_imputed, classification = TRUE) 
#> 
#> Type:                             Classification 
#> Number of trees:                  500 
#> Sample size:                      2207 
#> Number of independent variables:  7 
#> Mtry:                             2 
#> Target node size:                 1 
#> Variable importance mode:         none 
#> Splitrule:                        gini 
#> OOB prediction error:             19.76 %

Explainer for Titanic survival

The third step (it’s optional but useful) is to create a DALEX explainer for random forest model.

library("DALEX")
explain_titanic_rf <- explain(model_titanic_rf, 
                      data = titanic_imputed,
                      y = titanic_imputed$survived, 
                      label = "Random Forest v7",
                      colorize = FALSE)

#> Preparation of a new explainer is initiated
#>   -> model label       :  Random Forest v7 
#>   -> data              :  2207  rows  8  cols 
#>   -> target variable   :  2207  values 
#>   -> predict function  :  yhat.ranger  will be used (  default  )
#>   -> predicted values  :  numerical, min =  0 , mean =  0.2106932 , max =  1  
#>   -> model_info        :  package ranger , ver. 0.12.1 , task classification (  default  ) 
#>   -> residual function :  difference between y and yhat (  default  )
#>   -> residuals         :  numerical, min =  -1 , mean =  0.1114635 , max =  1  
#>   A new explainer has been created!

Variable importance plots

Use the variable_importance() explainer to present importance of particular features. Note that type = "difference" normalizes dropouts, and now they all start in 0.

vi_rf <- model_parts(explain_titanic_rf)
head(vi_rf)

#>       variable mean_dropout_loss            label
#> 1 _full_model_         0.2126564 Random Forest v7
#> 2     survived         0.2126677 Random Forest v7
#> 3        parch         0.2248505 Random Forest v7
#> 4        sibsp         0.2295760 Random Forest v7
#> 5     embarked         0.2317961 Random Forest v7
#> 6         fare         0.2484730 Random Forest v7

plot(vi_rf)

Variable effects

As we see the most important feature is Sex. Next three importnat features are Pclass, Age and Fare. Let’s see the link between model response and these features.

Such univariate relation can be calculated with variable_effect().

Age

Kids 5 years old and younger have much higher survival probability.

vr_age  <- model_profile(explain_titanic_rf, variables =  "age")
head(vr_age)

#> $cp_profiles
#> Top profiles    : 
#>       gender        age class    embarked fare sibsp parch survived _yhat_
#> 805     male  0.1666667   2nd Southampton 10.1     0     0        1      1
#> 805.1   male  2.0000000   2nd Southampton 10.1     0     0        1      1
#> 805.2   male  4.0000000   2nd Southampton 10.1     0     0        1      1
#> 805.3   male  7.0000000   2nd Southampton 10.1     0     0        1      1
#> 805.4   male  9.0000000   2nd Southampton 10.1     0     0        1      1
#> 805.5   male 13.0000000   2nd Southampton 10.1     0     0        1      0
#>       _vname_ _ids_          _label_
#> 805       age   805 Random Forest v7
#> 805.1     age   805 Random Forest v7
#> 805.2     age   805 Random Forest v7
#> 805.3     age   805 Random Forest v7
#> 805.4     age   805 Random Forest v7
#> 805.5     age   805 Random Forest v7
#> 
#> 
#> Top observations:
#>      gender age            class    embarked     fare sibsp parch survived
#> 805    male  19              2nd Southampton  10.1000     0     0        1
#> 1193   male  49              1st   Cherbourg 110.1708     1     1        0
#> 1394   male  34 victualling crew     Belfast   0.0000     0     0        0
#> 938    male  16              3rd Southampton  39.1309     4     1        0
#> 256  female  39              1st   Cherbourg  83.0302     1     1        1
#> 717    male  30              1st   Cherbourg  27.1405     0     0        0
#>      _yhat_          _label_ _ids_
#> 805       0 Random Forest v7     1
#> 1193      0 Random Forest v7     2
#> 1394      0 Random Forest v7     3
#> 938       0 Random Forest v7     4
#> 256       1 Random Forest v7     5
#> 717       0 Random Forest v7     6
#> 
#> $agr_profiles
#> Top profiles    : 
#>   _vname_          _label_        _x_ _yhat_ _ids_
#> 1     age Random Forest v7  0.1666667   0.50     0
#> 2     age Random Forest v7  2.0000000   0.62     0
#> 3     age Random Forest v7  4.0000000   0.61     0
#> 4     age Random Forest v7  7.0000000   0.52     0
#> 5     age Random Forest v7  9.0000000   0.45     0
#> 6     age Random Forest v7 13.0000000   0.29     0
#> 
#> $color
#> [1] "#4378bf"

plot(vr_age)

Passanger class

Passangers in the first class have much higher survival probability.

vr_class  <- model_profile(explain_titanic_rf, variables =  "class")
plot(vr_class)

Fare

Very cheap tickets are linked with lower chances.

vr_fare  <- variable_profile(explain_titanic_rf, variables =  "fare")
plot(vr_fare)

Embarked

Passangers that embarked from C have highest survival.

vr_embarked  <- model_profile(explain_titanic_rf, variables =  "embarked")
plot(vr_embarked)

Instance level explanations

Let’s see break down explanation for model predictions for 8 years old male from 1st class that embarked from port C.

new_passanger <- data.frame(
  class = factor("1st", levels = c("1st", "2nd", "3rd", "deck crew", "engineering crew", "restaurant staff", "victualling crew")),
  gender = factor("male", levels = c("female", "male")),
  age = 8,
  sibsp = 0,
  parch = 0,
  fare = 72,
  embarked = factor("Southampton", levels = c("Belfast", "Cherbourg", "Queenstown", "Southampton"))
)

sp_rf <- predict_parts(explain_titanic_rf, new_passanger)
plot(sp_rf)

It looks like the most important feature for this passenger is age and sex. After all his odds for survival are higher than for the average passenger. Mainly because of the young age and despite of being a male.

More models

Let’s train more models for survival.

Logistic regression

library("rms")
model_titanic_lmr <- lrm(survived ~ class + gender + rcs(age) + sibsp +
                   parch + fare + embarked, titanic_imputed)
explain_titanic_lmr <- explain(model_titanic_lmr, data = titanic_imputed, 
                   y = titanic_imputed$survived, 
                   predict_function = function(m,x) 
                            predict(m, x, type = "fitted"),
                   label = "Logistic regression")

#> Preparation of a new explainer is initiated
#>   -> model label       :  Logistic regression 
#>   -> data              :  2207  rows  8  cols 
#>   -> target variable   :  2207  values 
#>   -> predict function  :  function(m, x) predict(m, x, type = "fitted") 
#>   -> predicted values  :  numerical, min =  0.002671631 , mean =  0.3221568 , max =  0.9845724  
#>   -> model_info        :  package rms , ver. 6.0.0 , task classification ( [33m default [39m ) 
#>   -> residual function :  difference between y and yhat ( [33m default [39m )
#>   -> residuals         :  numerical, min =  -0.9845724 , mean =  -2.491758e-09 , max =  0.9715125  
#>  [32m A new explainer has been created! [39m

Generalized Boosted Models (GBM)

library("gbm")
model_titanic_gbm <- gbm(survived  ~ class + gender + age + sibsp +
                     parch + fare + embarked, data = titanic_imputed, 
                     n.trees = 15000)

#> Distribution not specified, assuming bernoulli ...

explain_titanic_gbm <- explain(model_titanic_gbm, data = titanic_imputed, 
                       y = titanic_imputed$survived, 
                       predict_function = function(m,x) 
                            predict(m, x, n.trees = 15000, type = "response"),
                       label = "Generalized Boosted Models",
                       colorize = FALSE)

#> Preparation of a new explainer is initiated
#>   -> model label       :  Generalized Boosted Models 
#>   -> data              :  2207  rows  8  cols 
#>   -> target variable   :  2207  values 
#>   -> predict function  :  function(m, x) predict(m, x, n.trees = 15000, type = "response") 
#>   -> predicted values  :  numerical, min =  0.0003325393 , mean =  0.3206172 , max =  0.9987133  
#>   -> model_info        :  package gbm , ver. 2.1.5 , task classification (  default  ) 
#>   -> residual function :  difference between y and yhat (  default  )
#>   -> residuals         :  numerical, min =  -0.9724482 , mean =  0.001539611 , max =  0.991273  
#>   A new explainer has been created!

Support Vector Machines (SVM)

library("e1071")
model_titanic_svm <- svm(survived ~ class + gender + age + sibsp +
                     parch + fare + embarked, data = titanic_imputed, 
             type = "C-classification", probability = TRUE)
explain_titanic_svm <- explain(model_titanic_svm, data = titanic_imputed, 
                       y = titanic_imputed$survived, 
                       label = "Support Vector Machines",
                       colorize = FALSE)

#> Preparation of a new explainer is initiated
#>   -> model label       :  Support Vector Machines 
#>   -> data              :  2207  rows  8  cols 
#>   -> target variable   :  2207  values 
#>   -> predict function  :  yhat.svm  will be used (  default  )
#>   -> predicted values  :  numerical, min =  0.08769275 , mean =  0.3233276 , max =  0.962329  
#>   -> model_info        :  package e1071 , ver. 1.7.3 , task classification (  default  ) 
#>   -> residual function :  difference between y and yhat (  default  )
#>   -> residuals         :  numerical, min =  -0.8652381 , mean =  -0.001170831 , max =  0.9123072  
#>   A new explainer has been created!

k-Nearest Neighbours (kNN)

library("caret")
model_titanic_knn <- knn3(survived ~ class + gender + age + sibsp +
                     parch + fare + embarked, data = titanic_imputed, k = 5)
explain_titanic_knn <- explain(model_titanic_knn, data = titanic_imputed, 
                       y = titanic_imputed$survived, 
                       predict_function = function(m,x) predict(m, x)[,2],
                       label = "k-Nearest Neighbours",
                       colorize = FALSE)

#> Preparation of a new explainer is initiated
#>   -> model label       :  k-Nearest Neighbours 
#>   -> data              :  2207  rows  8  cols 
#>   -> target variable   :  2207  values 
#>   -> predict function  :  function(m, x) predict(m, x)[, 2] 
#>   -> predicted values  :  numerical, min =  0 , mean =  0.3061413 , max =  1  
#>   -> model_info        :  package Model of class: knn3 package unrecognized , ver. Unknown , task regression (  default  ) 
#>   -> residual function :  difference between y and yhat (  default  )
#>   -> residuals         :  numerical, min =  -0.8333333 , mean =  0.01601551 , max =  0.9285714  
#>   A new explainer has been created!

Variable performance

vi_rf <- model_parts(explain_titanic_rf)
vi_lmr <- model_parts(explain_titanic_lmr)
vi_gbm <- model_parts(explain_titanic_gbm)
vi_svm <- model_parts(explain_titanic_svm)
vi_knn <- model_parts(explain_titanic_knn)

plot(vi_rf, vi_lmr, vi_gbm, vi_svm, vi_knn, bar_width = 4)

Single variable

vr_age_rf   <- model_profile(explain_titanic_rf, variables = "age")
vr_age_lmr  <- model_profile(explain_titanic_lmr, variables = "age")
vr_age_gbm  <- model_profile(explain_titanic_gbm, variables = "age")
vr_age_svm  <- model_profile(explain_titanic_svm, variables = "age")
vr_age_knn  <- model_profile(explain_titanic_knn, variables = "age")
plot(vr_age_rf$agr_profiles, 
     vr_age_lmr$agr_profiles, 
     vr_age_gbm$agr_profiles, 
     vr_age_svm$agr_profiles, 
     vr_age_knn$agr_profiles)

Instance level explanations

sp_rf <- predict_parts(explain_titanic_rf, new_passanger)
plot(sp_rf)

sp_lmr <- predict_parts(explain_titanic_lmr, new_passanger)
plot(sp_lmr)

sp_gbm <- predict_parts(explain_titanic_gbm, new_passanger)
plot(sp_gbm)

sp_svm <- predict_parts(explain_titanic_svm, new_passanger)
plot(sp_svm)

sp_knn <- predict_parts(explain_titanic_knn, new_passanger)
plot(sp_knn)

Session info

sessionInfo()

#> R version 4.0.2 (2020-06-22)
#> Platform: x86_64-apple-darwin17.0 (64-bit)
#> Running under: macOS Catalina 10.15.5
#> 
#> Matrix products: default
#> BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
#> 
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#>  [1] caret_6.0-86    e1071_1.7-3     gbm_2.1.5       rms_6.0-0      
#>  [5] SparseM_1.78    Hmisc_4.4-0     ggplot2_3.3.2   Formula_1.2-3  
#>  [9] survival_3.1-12 lattice_0.20-41 ranger_0.12.1   DALEX_1.3.0    
#> 
#> loaded via a namespace (and not attached):
#>  [1] foreach_1.5.0        splines_4.0.2        prodlim_2019.11.13  
#>  [4] assertthat_0.2.1     stats4_4.0.2         ingredients_1.3.0   
#>  [7] latticeExtra_0.6-29  yaml_2.2.1           ipred_0.9-9         
#> [10] pillar_1.4.4         backports_1.1.8      quantreg_5.55       
#> [13] glue_1.4.1           pROC_1.16.2          digest_0.6.25       
#> [16] RColorBrewer_1.1-2   checkmate_2.0.0      recipes_0.1.13      
#> [19] colorspace_1.4-1     sandwich_2.5-1       plyr_1.8.6          
#> [22] htmltools_0.5.0      Matrix_1.2-18        timeDate_3043.102   
#> [25] pkgconfig_2.0.3      purrr_0.3.4          mvtnorm_1.1-1       
#> [28] scales_1.1.1         gower_0.2.2          jpeg_0.1-8.1        
#> [31] lava_1.6.7           MatrixModels_0.4-1   htmlTable_2.0.0     
#> [34] tibble_3.0.1         generics_0.0.2       farver_2.0.3        
#> [37] ellipsis_0.3.1       TH.data_1.0-10       withr_2.2.0         
#> [40] nnet_7.3-14          magrittr_1.5         crayon_1.3.4        
#> [43] memoise_1.1.0        polspline_1.1.19     evaluate_0.14       
#> [46] fs_1.4.2             nlme_3.1-148         MASS_7.3-51.6       
#> [49] foreign_0.8-80       class_7.3-17         tools_4.0.2         
#> [52] data.table_1.12.8    lifecycle_0.2.0      multcomp_1.4-13     
#> [55] stringr_1.4.0        munsell_0.5.0        cluster_2.1.0       
#> [58] compiler_4.0.2       pkgdown_1.5.1.9000   rlang_0.4.6         
#> [61] grid_4.0.2           iterators_1.0.12     rstudioapi_0.11     
#> [64] htmlwidgets_1.5.1    base64enc_0.1-3      labeling_0.3        
#> [67] rmarkdown_2.3.2      ModelMetrics_1.2.2.2 gtable_0.3.0        
#> [70] codetools_0.2-16     reshape2_1.4.4       R6_2.4.1            
#> [73] lubridate_1.7.9      gridExtra_2.3        zoo_1.8-8           
#> [76] knitr_1.29           dplyr_1.0.0          rprojroot_1.3-2     
#> [79] iBreakDown_1.2.0     desc_1.2.0           stringi_1.4.6       
#> [82] Rcpp_1.0.4.6         vctrs_0.3.1          rpart_4.1-15        
#> [85] acepack_1.4.1        png_0.1-7            tidyselect_1.1.0    
#> [88] xfun_0.15

Survival on the RMS Titanic

Przemyslaw Biecek

2020-07-02

Data for Titanic survival

Model for Titanic survival

Explainer for Titanic survival

Variable importance plots

Variable effects

Age

Passanger class

Fare

Embarked

Instance level explanations

More models

Logistic regression

Generalized Boosted Models (GBM)

Support Vector Machines (SVM)

k-Nearest Neighbours (kNN)

Variable performance

Single variable

Instance level explanations

Session info