ale: Accumulated Local Effects (ALE)

In effectplots: Effect Plots

Accumulated Local Effects (ALE)

Description

Calculates ALE for one or multiple continuous features specified by X.

The concept of ALE was introduced in Apley et al. (2020) as an alternative to partial dependence (PD). The Ceteris Paribus clause behind PD is a blessing and a curse at the same time:

• Blessing: The interpretation is easy and similar to what we know from linear regression (just averaging out interaction effects).

• Curse: The model is applied to very unlikely or even impossible feature combinations, especially with strongly dependent features.

ALE fixes the curse as follows: Per bin, the local effect is calculated as the partial dependence difference between lower and upper bin break, using only observations falling into this bin. This is repeated for all bins, and the values are accumulated.

ALE values are plotted against right bin breaks.

Usage

ale(object, ...)

## Default S3 method:
ale(
  object,
  v,
  data,
  pred_fun = stats::predict,
  trafo = NULL,
  which_pred = NULL,
  w = NULL,
  breaks = "Sturges",
  right = TRUE,
  discrete_m = 13L,
  outlier_iqr = 2,
  ale_n = 50000L,
  ale_bin_size = 200L,
  seed = NULL,
  ...
)

## S3 method for class 'ranger'
ale(
  object,
  v,
  data,
  pred_fun = NULL,
  trafo = NULL,
  which_pred = NULL,
  w = NULL,
  breaks = "Sturges",
  right = TRUE,
  discrete_m = 13L,
  outlier_iqr = 2,
  ale_n = 50000L,
  ale_bin_size = 200L,
  seed = NULL,
  ...
)

## S3 method for class 'explainer'
ale(
  object,
  v = colnames(data),
  data = object$data,
  pred_fun = object$predict_function,
  trafo = NULL,
  which_pred = NULL,
  w = object$weights,
  breaks = "Sturges",
  right = TRUE,
  discrete_m = 13L,
  outlier_iqr = 2,
  ale_n = 50000L,
  ale_bin_size = 200L,
  seed = NULL,
  ...
)

## S3 method for class 'H2OModel'
ale(
  object,
  data,
  v = object@parameters$x,
  pred_fun = NULL,
  trafo = NULL,
  which_pred = NULL,
  w = object@parameters$weights_column$column_name,
  breaks = "Sturges",
  right = TRUE,
  discrete_m = 13L,
  outlier_iqr = 2,
  ale_n = 50000L,
  ale_bin_size = 200L,
  seed = NULL,
  ...
)

Arguments

object	Fitted model.
...	Further arguments passed to pred_fun(), e.g., type = "response" in a glm() or (typically) prob = TRUE in classification models.
v	Variable names to calculate statistics for.
data	Matrix or data.frame.
pred_fun	Prediction function, by default stats::predict. The function takes three arguments (names irrelevant): object, data, and ....
trafo	How should predictions be transformed? A function or NULL (default). Examples are log (to switch to link scale) or exp (to switch from link scale to the original scale). Applied after which_pred.
which_pred	If the predictions are multivariate: which column to pick (integer or column name). By default NULL (picks last column). Applied before trafo.
w	Optional vector with case weights. Can also be a column name in data. Having observations with non-positive weight is equivalent to excluding them.
breaks	An integer, vector, or "Sturges" (the default) used to determine bin breaks of continuous features. Values outside the total bin range are placed in the outmost bins. To allow varying values of breaks across features, breaks can be a list of the same length as v, or a named list with breaks for certain variables.
right	Should bins be right-closed? The default is TRUE. Vectorized over v. Only relevant for continuous features.
discrete_m	Numeric features with up to this number of unique values are treated as discrete and are therefore dropped from the calculations.
outlier_iqr	If breaks is an integer or "Sturges", the breaks of a continuous feature are calculated without taking into account feature values outside quartiles +- outlier_iqr * IQR (where <= 9997 values are used to calculate the quartiles). To let the breaks cover the full data range, set outlier_iqr to 0 or Inf. Vectorized over v.
ale_n	Size of the data used for calculating ALE. The default is 50000. For larger data (and w), ale_n rows are randomly sampled. Each variable specified by v uses the same sample. Set to 0 to omit ALE calculations.
ale_bin_size	Maximal number of observations used per bin for ALE calculations. If there are more observations in a bin, ale_bin_size indices are randomly sampled. The default is 200. Applied after sampling regarding ale_n.
seed	Optional integer random seed used for: ALE: select background data if n > ale_n, and for bins > ale_bin_size. Calculating breaks: The bin range is determined without values outside quartiles +- 2 IQR using a sample of <= 9997 observations to calculate quartiles.

Details

The function is a convenience wrapper around feature_effects(), which calls the barebone implementation .ale() to calculate ALE.

Value

A list (of class "EffectData") with a data.frame per feature having columns:

• bin_mid: Bin mid points. In the plots, the bars are centered around these.

• bin_width: Absolute width of the bin. In the plots, these equal the bar widths.

• bin_mean: For continuous features, the (possibly weighted) average feature value within bin. For discrete features equivalent to bin_mid.

• N: The number of observations within bin.

• weight: The weight sum within bin. When w = NULL, equivalent to N.

• Different statistics, depending on the function call.

Use single bracket subsetting to select part of the output. Note that each data.frame contains an attribute "discrete" with the information whether the feature is discrete or continuous. This attribute might be lost when you manually modify the data.frames.

Methods (by class)

• ale(default): Default method.

• ale(ranger): Method for ranger models.

• ale(explainer): Method for DALEX explainers

• ale(H2OModel): Method for H2O models

References

Apley, Daniel W., and Jingyu Zhu. 2020. Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82 (4): 1059–1086. doi:10.1111/rssb.12377.

See Also

feature_effects(), .ale()

Examples

fit <- lm(Sepal.Length ~ ., data = iris)
M <- ale(fit, v = "Petal.Length", data = iris)
M |> plot()

M2 <- ale(fit, v = colnames(iris)[-1], data = iris, breaks = 5)
plot(M2, share_y = "all")  # Only continuous variables shown

effectplots documentation built on April 12, 2025, 2:13 a.m.