iml (version 0.1)

ice: Individual conditional expectations (ICE)

Description

Fits and plots individual conditional expectation function on an arbitrary machine learning model

Usage

ice(object, X, feature, grid.size = 10, center.at = NULL, class = NULL,
  ...)

Arguments

object

The machine learning model. Different types are allowed. Recommended are mlr WrappedModel and caret train objects. The object can also be a function that predicts the outcome given features or anything with an S3 predict function, like an object from class lm.

X

data.frame with the data for the prediction model

feature

The index of the feature of interest.

grid.size

The size of the grid for evaluating the predictions

center.at

The value for the centering of the plot. Numeric for numeric features, and the level name for factors.

class

In case of classification, class specifies the class for which to predict the probability. By default the multiclass classification is done.

...

Further arguments for the prediction method.

Value

An individual conditional expectation object

An ICE object (R6). Its methods and variables can be accessed with the $-operator:

feature.name

The feature name for which the partial dependence was computed.

feature.type

The detected type of the feature, either "categorical" or "numerical".

feature.index

The index of the feature for which the individual conditional expectations weree computed.

center.at

The features value(s) at which the ice computations are centered.

grid.size

The size of the grid.

sample.size

The number of instances sampled from data X.

center

method to get/set the feature value at which the ice computation should be centered. See examples for usage.

feature

method to get/set the feature (index) for which to compute ice. See examples for usage.

data()

method to extract the results of the partial dependence plot. Returns a data.frame with the grid of feature of interest and the predicted \(\hat{y}\). Can be used for creating custom partial dependence plots.

plot()

method to plot the partial dependence function. See plot.PDP

Details

Machine learning model try to learn the relationship \(y = f(X)\). We can't visualize the learned \(\hat{f}\) directly for an individual, high-dimensional point \(x_i\).

But we can take one of the input features of an observation and change its value. We try out a grid of different values and observe the predicted outcome. This gives us the predicted \(\hat{y}\) as a function of feature \(X_j\), which we can plot as a line. The ice method repeats this for all the observations in the dataset and plots all the lines in the same plot.

Mathematically, we split up the learned function into its parts: $$f(x_i) = f_1(x_{i,1}) + \ldots + f_p(x_{i,p}) + f_{1, 2}(x_{i,1}, x_{i,2}) + \ldots + f_{p-1, p}(x_{i,p-1}, x_{p}) + \ldots + f_{1\ldots p}(x_{i,1\ldots X_p})$$,

And we can isolate the individual conditional expectation of \(y\) on a single \(X_j\): \(f_j(X_j)\) and plot it.

Partial dependence plots (pdp) are the averaged lines of ice curves. The returned object can be plotted is a ggplot object. This means it can be plotted directly or be extended using ggplots + operator. To learn more about partial dependence plot, read the Interpretable Machine Learning book: https://christophm.github.io/interpretable-ml-book/ice.html

References

Goldstein, A., Kapelner, A., Bleich, J., and Pitkin, E. (2013). Peeking Inside the Black Box: Visualizing Statistical Learning with Plots of Individual Conditional Expectation, 1-22. https://doi.org/10.1080/10618600.2014.907095

See Also

pdp for partial dependence plots (aggregated ice plots)

Examples

# NOT RUN {
# We train a random forest on the Boston dataset:
if(require("randomForest")){

data("Boston", package  = "MASS")
mod = randomForest(medv ~ ., data = Boston, ntree = 50)

# Compute the individual conditional expectations for the first feature
ice.obj = ice(mod, Boston, feature = 1)

# Plot the results directly
plot(ice.obj)

# You can center the ICE plot
ice.obj$center.at = 0
plot(ice.obj)

# ICE plots can be centered at initialization
ice.obj = ice(mod, Boston, feature = 1, center=75)
plot(ice.obj)

# Centering can also be removed
ice.obj$center.at = NULL
plot(ice.obj)

# Since the result is a ggplot object, you can extend it: 
library("ggplot2")
plot(ice.obj) + theme_bw()

# If you want to do your own thing, just extract the data: 
ice.dat = ice.obj$data()
head(ice.dat)
ggplot(ice.dat) + 
geom_line(aes(x = crim, y = y.hat, group = ..individual, color = factor(..individual))) + 
scale_color_discrete(guide = "none")

# You can reuse the ice object for other features: 
ice.obj$feature = 2
plot(ice.obj)

# ICE also works with multiclass classification
library("randomForest")
mod = randomForest(Species ~ ., data= iris, ntree=50)

# For some models we have to specify additional arguments for the predict function
plot(ice(mod, iris, feature = 1, predict.args = list(type = 'prob')))

# For multiclass classification models, you can choose to only show one class:
plot(ice(mod, iris, feature = 1, class = 1, predict.args = list(type = 'prob')))

# ICE plots can be centered: 
plot(ice(mod, iris, feature = 1, center = 1, predict.args = list(type = 'prob')))
}
# }