Package 'xgrove'

Plot surrogate tree statistics

Description

Plot statistics of surrogate trees to analyze complexity vs. explanatory power.

Usage

## S3 method for class 'sgtree'
plot(x, abs = "rules", ord = "upsilon", ...)

Arguments

x	An object of class sgtree.
abs	Name of the measure to be plotted on the x-axis, either "trees", "rules", "upsilon" or "cor".
ord	Name of the measure to be plotted on the y-axis, either "trees", "rules", "upsilon" or "cor".
...	Further arguments passed to plot.

Value

No return value.

Author(s)

[email protected]

Examples

library(randomForest)
library(pdp)
data(boston)
set.seed(42)
rf <- randomForest(cmedv ~ ., data = boston)
data <- boston[,-3] # remove target variable
ntrees <- c(4,8,16,32,64,128)
xg <- xgrove(rf, data, ntrees)
xg
plot(xg)

---

Plot surrogate grove statistics

Description

Plot statistics of surrogate groves to analyze complexity vs. explanatory power.

Usage

## S3 method for class 'xgrove'
plot(x, abs = "rules", ord = "upsilon", ...)

Arguments

x	An object of class xgrove.
abs	Name of the measure to be plotted on the x-axis, either "trees", "rules", "upsilon" or "cor".
ord	Name of the measure to be plotted on the y-axis, either "trees", "rules", "upsilon" or "cor".
...	Further arguments passed to plot.

Value

No return value.

Author(s)

[email protected]

Examples

library(randomForest)
library(pdp)
data(boston)
set.seed(42)
rf <- randomForest(cmedv ~ ., data = boston)
data <- boston[,-3] # remove target variable
ntrees <- c(4,8,16,32,64,128)
xg <- xgrove(rf, data, ntrees)
xg
plot(xg)

---

Surrogate trees

Description

Compute surrogate trees of different depth to explain predictive machine learning model and analyze complexity vs. explanatory power.

Usage

sgtree(model, data, maxdeps = 1:8, cparam = 0, pfun = NULL, ...)

Arguments

model	A model with corresponding predict function that returns numeric values.
data	Data that must not (!) contain the target variable.
maxdeps	Sequence of integers: Maximum depth of the trees.
cparam	Complexity parameter for growing the trees.
pfun	Optional predict function function(model, data) returning a real number. Default is the predict() method of the model.
...	Further arguments to be passed to rpart.control or the predict() method of the model.

Details

A surrogate grove is trained via gradient boosting using rpart on data with the predictions of using of the model as target variable. Note that data must not contain the original target variable!

Value

List of the results:

explanation	Matrix containing tree sizes, rules, explainability ${\Upsilon}$ and the correlation between the predictions of the explanation and the true model.
rules	List of rules for each tree.
model	List of the rpart models.

Author(s)

[email protected]

References

• Szepannek, G. and Laabs, B.H. (2023): Can’t see the forest for the trees – analyzing groves to explain random forests, Behaviormetrika, submitted.

• Szepannek, G. and Luebke, K.(2023): How much do we see? On the explainability of partial dependence plots for credit risk scoring, Argumenta Oeconomica 50, DOI: 10.15611/aoe.2023.1.07.

Examples

library(randomForest)
library(pdp)
data(boston)
set.seed(42)
rf    <- randomForest(cmedv ~ ., data = boston)
data  <- boston[,-3] # remove target variable
maxds <- 1:7
st    <- sgtree(rf, data, maxds)
st
# rules for tree of depth 3
st$rules[["3"]]
# plot tree of depth 3
rpart.plot::rpart.plot(st$model[["3"]])

---

Explainability

Description

Compute explainability given predicted data of the model and an explainer.

Usage

upsilon(porig, pexp)

Arguments

porig	An object of class xgrove.
pexp	Name of the measure to be plotted on the x-axis, either "trees", "rules", "upsilon" or "cor".

Value

Numeric explainability upsilon.

Author(s)

[email protected]

References

• Szepannek, G. and Luebke, K.(2023): How much do we see? On the explainability of partial dependence plots for credit risk scoring, Argumenta Oeconomica 50, DOI: 10.15611/aoe.2023.1.07.

Examples

library(randomForest)
library(pdp)
data(boston)
set.seed(42)
# Compute original model
rf <- randomForest(cmedv ~ ., data = boston)
data <- boston[,-3] # remove target variable
# Compute predictions
porig <- predict(rf, data)

# Compute surrogate grove
xg <- xgrove(rf, data)
pexp <- predict(xg$model, data, n.trees = 16)
upsilon(porig, pexp)

---

Explanation groves

Description

Compute surrogate groves to explain predictive machine learning model and analyze complexity vs. explanatory power.

Usage

xgrove(
  model,
  data,
  ntrees = c(4, 8, 16, 32, 64, 128),
  pfun = NULL,
  remove.target = T,
  shrink = 1,
  b.frac = 1,
  seed = 42,
  ...
)

Arguments

model	A model with corresponding predict function that returns numeric values.
data	Training data.
ntrees	Sequence of integers: number of boosting trees for rule extraction.
pfun	Optional predict function function(model, data) returning a real number. Default is the predict() method of the model.
remove.target	Logical. If TRUE the name of the target variable is identified from terms(model) and automatically removed if this variable is still in data.
shrink	Sets the shrinkage argument for the internal call of gbm. As the model usually has a deterministic response the default is 1 different to the default of gbm applied train a model based on data.
b.frac	Sets the bag.fraction argument for the internal call of gbm. As the model usually has a deterministic response the default is 1 different to the default of gbm applied train a model based on data.
seed	Seed for the random number generator to ensure reproducible results (e.g. for the default bag.fraction < 1 in boosting).
...	Further arguments to be passed to gbm or the predict() method of the model.

Details

A surrogate grove is trained via gradient boosting using gbm on data with the predictions of using of the model as target variable. Note that data must not contain the original target variable! The boosting model is trained using stumps of depth 1. The resulting interpretation is extracted from pretty.gbm.tree. The column upper_bound_left of the rules and the groves value of the output object contains the split point for numeric variables denoting the uppoer bound of the left branch. Correspondingly, the levels_left column contains the levels of factor variables assigned to the left branch. The rule weights of the branches are given in the rightmost columns. The prediction of the grove is obtained as the sum of the assigned weights over all rows. Note that the training data must not contain the target variable. It can be either removed manually or will be removed automatically from data if the argument remove.target == TRUE.

Value

List of the results:

explanation	Matrix containing tree sizes, rules, explainability ${\Upsilon}$ and the correlation between the predictions of the explanation and the true model.
rules	Summary of the explanation grove: Rules with identical splits are aggegated. For numeric variables any splits are merged if they lead to identical parititions of the training data.
groves	Rules of the explanation grove.
model	gbm model.

Author(s)

[email protected]

References

• Szepannek, G. and von Holt, B.H. (2023): Can’t see the forest for the trees – analyzing groves to explain random forests, Behaviormetrika, DOI: 10.1007/s41237-023-00205-2.

• Szepannek, G. and Luebke, K.(2023): How much do we see? On the explainability of partial dependence plots for credit risk scoring, Argumenta Oeconomica 50, DOI: 10.15611/aoe.2023.1.07.

Examples

library(randomForest)
library(pdp)
data(boston)
set.seed(42)
rf <- randomForest(cmedv ~ ., data = boston)
data <- boston[,-3] # remove target variable
ntrees <- c(4,8,16,32,64,128)
xg <- xgrove(rf, data, ntrees)
xg
plot(xg)

# Example of a classification problem using the iris data.
# A predict function has to be defined, here for the posterior probabilities of the class Virginica.  
data(iris)
set.seed(42)
rf    <- randomForest(Species ~ ., data = iris)
data  <- iris[,-5] # remove target variable

pf <- function(model, data){
  predict(model, data, type = "prob")[,3]
  }
  
xgrove(rf, data, pfun = pf)

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