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-A set of tools to understand what is happening inside a Random Forest. A detailed discussion of the package and importance measures it implements can be found here: [Master thesis on randomForestExplainer](https://cdn.staticaly.com/gh/geneticsMiNIng/BlackBoxOpener/master/randomForestExplainer_Master_thesis.pdf).
+A set of tools to understand what is happening inside a Random Forest. A detailed discussion of the package and importance measures it implements can be found here: [Master thesis on randomForestExplainer](https://github.com/geneticsMiNIng/BlackBoxOpener/blob/master/randomForestExplainer_Master_thesis.pdf).
## Installation
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Understanding random forests with randomForestExplainer
-Aleksandra Paluszyńska
+Understanding random forests with +randomForestExplainer
+Aleksandra +Paluszyńska
- Source:vignettes/randomForestExplainer.Rmd+ Source:vignettes/randomForestExplainer.RmdrandomForestExplainer.Rmd---Introduction
-This vignette demonstrates how to use the randomForestExplainer package. We will use the
+Bostonfrom packageMASS. In fact, the development of randomForestExplainer was motivated by problems that include lots of predictors and not many observations. However, as they usually require growing large forests and are computationally intensive, we use the smallBostondata set here and encourage you to follow our analysis of such large data set concerning glioblastoma here: initial vignette.+Introduction +
+This vignette demonstrates how to use the randomForestExplainer +package. We will use the
Bostonfrom package +MASS. In fact, the development of randomForestExplainer was +motivated by problems that include lots of predictors and not many +observations. However, as they usually require growing large forests and +are computationally intensive, we use the smallBostondata +set here and encourage you to follow our analysis of such large data set +concerning glioblastoma here: initial +vignette.We will use the following packages:
+-
library(randomForest) -# devtools::install_github("MI2DataLab/randomForestExplainer") -library(randomForestExplainer)library(randomForest) +# devtools::install_github("MI2DataLab/randomForestExplainer") +library(randomForestExplainer)-+-Data and forest
+++Data and forest +
The data set
Bostonhas the following structure:--
data(Boston, package = "MASS") -Boston$chas <- as.logical(Boston$chas) -str(Boston)
-## 'data.frame': 506 obs. of 14 variables: -## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ... -## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ... -## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ... -## $ chas : logi FALSE FALSE FALSE FALSE FALSE FALSE ... -## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ... -## $ rm : num 6.58 6.42 7.18 7 7.15 ... -## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ... -## $ dis : num 4.09 4.97 4.97 6.06 6.06 ... -## $ rad : int 1 2 2 3 3 3 5 5 5 5 ... -## $ tax : num 296 242 242 222 222 222 311 311 311 311 ... -## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ... -## $ black : num 397 397 393 395 397 ... -## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ... -## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...We use the
+randomForest::randomForestfunction to train a forest of \(B=500\) trees (default value of themtryparameter of this function), with optionlocalImp = TRUE. The forest is supposed to predict the median price of an apartmentmedvbased on its characteristics.data(Boston, package = "MASS") +Boston$chas <- as.logical(Boston$chas) +str(Boston)
+## 'data.frame': 506 obs. of 14 variables: +## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ... +## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ... +## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ... +## $ chas : logi FALSE FALSE FALSE FALSE FALSE FALSE ... +## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ... +## $ rm : num 6.58 6.42 7.18 7 7.15 ... +## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ... +## $ dis : num 4.09 4.97 4.97 6.06 6.06 ... +## $ rad : int 1 2 2 3 3 3 5 5 5 5 ... +## $ tax : num 296 242 242 222 222 222 311 311 311 311 ... +## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ... +## $ black : num 397 397 393 395 397 ... +## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ... +## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...We use the
randomForest::randomForestfunction to train +a forest of \(B=500\) trees (default +value of themtryparameter of this function), with option +localImp = TRUE. The forest is supposed to predict the +median price of an apartmentmedvbased on its +characteristics.--
set.seed(2017) -forest <- randomForest(medv ~ ., data = Boston, localImp = TRUE)The prediction accuracy of our forest can be summarized as follows:
+set.seed(2017) +forest <- randomForest(medv ~ ., data = Boston, localImp = TRUE)The prediction accuracy of our forest can be summarized as +follows:
--
forest
-## -## Call: -## randomForest(formula = medv ~ ., data = Boston, localImp = TRUE) -## Type of random forest: regression -## Number of trees: 500 -## No. of variables tried at each split: 4 -## -## Mean of squared residuals: 9.793518 -## % Var explained: 88.4Now, we will use all the functions of
+randomForestExplainerin turn and comment on the obtained results.forest
+## +## Call: +## randomForest(formula = medv ~ ., data = Boston, localImp = TRUE) +## Type of random forest: regression +## Number of trees: 500 +## No. of variables tried at each split: 4 +## +## Mean of squared residuals: 9.793518 +## % Var explained: 88.4Now, we will use all the functions of +
randomForestExplainerin turn and comment on the obtained +results.--Distribution of minimal depth
-To obtain the distribution of minimal depth we pass our forest to the function
+min_depth_distributionand store the result, which contains the following columns (we save this and load it from memory as it takes a while):++Distribution of minimal depth +
+To obtain the distribution of minimal depth we pass our forest to the +function
min_depth_distributionand store the result, which +contains the following columns (we save this and load it from memory as +it takes a while):--
# min_depth_frame <- min_depth_distribution(forest) -# save(min_depth_frame, file = "min_depth_frame.rda") -load("min_depth_frame.rda") -head(min_depth_frame, n = 10)
-## tree variable minimal_depth -## 1 1 age 4 -## 2 1 black 3 -## 3 1 chas 10 -## 4 1 crim 4 -## 5 1 dis 1 -## 6 1 indus 4 -## 7 1 lstat 1 -## 8 1 nox 2 -## 9 1 ptratio 3 -## 10 1 rad 6Next, we pass it to the function
+plot_min_depth_distributionand under default settings obtain obtain a plot of the distribution of minimal depth for top ten variables according to mean minimal depth calculated using top trees (mean_sample = "top_trees"). We could also pass our forest directly to the plotting function but if we want to make more than one plot of the minimal depth distribution is more efficient to pass themin_depth_frameto the plotting function so that it will not be calculated again for each plot (this works similarly for other plotting functions ofrandomForestExplainer).# min_depth_frame <- min_depth_distribution(forest) +# save(min_depth_frame, file = "min_depth_frame.rda") +load("min_depth_frame.rda") +head(min_depth_frame, n = 10)
+## tree variable minimal_depth +## 1 1 age 4 +## 2 1 black 3 +## 3 1 chas 10 +## 4 1 crim 4 +## 5 1 dis 1 +## 6 1 indus 4 +## 7 1 lstat 1 +## 8 1 nox 2 +## 9 1 ptratio 3 +## 10 1 rad 6Next, we pass it to the function +
plot_min_depth_distributionand under default settings +obtain obtain a plot of the distribution of minimal depth for top ten +variables according to mean minimal depth calculated using top trees +(mean_sample = "top_trees"). We could also pass our forest +directly to the plotting function but if we want to make more than one +plot of the minimal depth distribution is more efficient to pass the +min_depth_frameto the plotting function so that it will +not be calculated again for each plot (this works similarly for other +plotting functions ofrandomForestExplainer).+-
# plot_min_depth_distribution(forest) # gives the same result as below but takes longer -plot_min_depth_distribution(min_depth_frame)# plot_min_depth_distribution(forest) # gives the same result as below but takes longer +plot_min_depth_distribution(min_depth_frame)
-
The function
+plot_min_depth_distributionoffers three possibilities when it comes to calculating the mean minimal depth, which differ in he way they treat missing values that appear when a variable is not used for splitting in a tree. They can be described as follows:The function
plot_min_depth_distributionoffers three +possibilities when it comes to calculating the mean minimal depth, which +differ in he way they treat missing values that appear when a variable +is not used for splitting in a tree. They can be described as +follows:-
-
mean_sample = "all_trees"(filling missing value): the minimal depth of a variable in a tree that does not use it for splitting is equal to the mean depth of trees. Note that the depth of a tree is equal to the length of the longest path from root to leave in this tree. This equals the maximum depth of a variable in this tree plus one, as leaves are by definition not split by any variable.
-mean_sample = "top_trees"(restricting the sample): to calculate the mean minimal depth only \(\tilde{B}\) out of \(B\) (number of trees) observations are considered, where \(\tilde{B}\) is equal to the maximum number of trees in which any variable was used for splitting. Remaining missing values for variables that were used for splitting less than \(\tilde{B}\) times are filled in as inmean_sample = "all_trees".
-mean_sample = "relevant_trees"(ignoring missing values): mean minimal depth is calculated using only non-missing values.
+mean_sample = "all_trees"(filling missing value): +the minimal depth of a variable in a tree that does not use it for +splitting is equal to the mean depth of trees. Note that the depth of a +tree is equal to the length of the longest path from root to leave in +this tree. This equals the maximum depth of a variable in this tree plus +one, as leaves are by definition not split by any variable.
+mean_sample = "top_trees"(restricting the sample): +to calculate the mean minimal depth only \(\tilde{B}\) out of \(B\) (number of trees) observations are +considered, where \(\tilde{B}\) is +equal to the maximum number of trees in which any variable was used for +splitting. Remaining missing values for variables that were used for +splitting less than \(\tilde{B}\) times +are filled in as inmean_sample = "all_trees".
+mean_sample = "relevant_trees"(ignoring missing +values): mean minimal depth is calculated using only non-missing +values.
Note that the \(x\)-axis ranges from zero trees to the maximum number of trees in which any variable was used for splitting (\(\tilde{B}\)) which is in this case equal to 500 and is reached by all variables plotted.
-The ordering of variables in our plot by their mean minimal depth seems quite accurate when we look at the distribution of minimal depth, though one could argue that for example
+indusshould be ranked higher thandisas the latter is never used for splitting at the root. Usually we would obtain different orderings when changing themean_sampleoption but this is not the case if variables are used for splitting in all trees as this option only influences how and whether missing values are treated. The default option,"top_trees", penalizes missing values and this penalization makes the interpretation of the values less obvious – to address that we can calculate the mean minimal depth only using non-missing observations (mean_sample = "relevant_trees"). For forests with many variables with a lot of missing observations we should always consider adding themin_no_of_treesoption so that only variables used for splitting in at least the declared number of trees will be considered for the plot. This allows us to avoid selecting variables that have been by chance used for splitting e.g., only once but at the root (their mean would be equal to 0). However, in our case we can simply increase thekparameter to plot all trees:Note that the \(x\)-axis ranges from +zero trees to the maximum number of trees in which any variable was used +for splitting (\(\tilde{B}\)) which is +in this case equal to 500 and is reached by all variables plotted.
+The ordering of variables in our plot by their mean minimal depth +seems quite accurate when we look at the distribution of minimal depth, +though one could argue that for example
indusshould be +ranked higher thandisas the latter is never used for +splitting at the root. Usually we would obtain different orderings when +changing themean_sampleoption but this is not the case if +variables are used for splitting in all trees as this option only +influences how and whether missing values are treated. The default +option,"top_trees", penalizes missing values and this +penalization makes the interpretation of the values less obvious – to +address that we can calculate the mean minimal depth only using +non-missing observations (mean_sample = "relevant_trees"). +For forests with many variables with a lot of missing observations we +should always consider adding themin_no_of_treesoption so +that only variables used for splitting in at least the declared number +of trees will be considered for the plot. This allows us to avoid +selecting variables that have been by chance used for splitting e.g., +only once but at the root (their mean would be equal to 0). However, in +our case we can simply increase thekparameter to plot all +trees:+-
plot_min_depth_distribution(min_depth_frame, mean_sample = "relevant_trees", k = 15)plot_min_depth_distribution(min_depth_frame, mean_sample = "relevant_trees", k = 15)
-
Clearly, using only relevant trees for calculating the mean does not change it for variables that have no missing values. Also, in this case the change does not influence the ordering of variables, but of course this usually not the case in more complex examples.
-Regardless of the exact parameters used in
+plot_min_depth_distribution, looking at the whole distribution of minimal depth offers a lot more insight into the role that a predictor plays in a forest in contrast to looking only at the mean, especially as it can be calculated in more than one way. Additionally, the function allows us to specify the maximum number of variables plottedk, whether the values of mean minimal depth should be scaled to the \([0,1]\) interval (mean_scale, logical), the number of digits to round the mean to for display (mean_round) and the title of the plot (main).Clearly, using only relevant trees for calculating the mean does not +change it for variables that have no missing values. Also, in this case +the change does not influence the ordering of variables, but of course +this usually not the case in more complex examples.
+Regardless of the exact parameters used in +
plot_min_depth_distribution, looking at the whole +distribution of minimal depth offers a lot more insight into the role +that a predictor plays in a forest in contrast to looking only at the +mean, especially as it can be calculated in more than one way. +Additionally, the function allows us to specify the maximum number of +variables plottedk, whether the values of mean minimal +depth should be scaled to the \([0,1]\) +interval (mean_scale, logical), the number of digits to +round the mean to for display (mean_round) and the title of +the plot (main).
+
