Partial Dependence

Calculates PD for one or multiple features.

PD was introduced by Friedman (2001) to study the (main) effects of a ML model. PD of a model f and variable X at a certain value g is derived by replacing the X values in a reference data by g, and then calculating the average prediction of f over this modified data. This is done for different g to see how the average prediction of f changes in X, keeping all other feature values constant (Ceteris Paribus).

This function is a convenience wrapper around feature_effects(), which calls the barebone implementation .pd() to calculate PD. As grid points, it uses the arithmetic mean of X per bin (specified by breaks), and eventually weighted by w.

partial_dependence(object, ...)

# Default S3 method
partial_dependence(
  object,
  v,
  data,
  pred_fun = stats::predict,
  trafo = NULL,
  which_pred = NULL,
  w = NULL,
  breaks = "Sturges",
  right = TRUE,
  discrete_m = 13L,
  outlier_iqr = 2,
  pd_n = 500L,
  seed = NULL,
  ...
)

# S3 method for class 'ranger'
partial_dependence(
  object,
  v,
  data,
  pred_fun = NULL,
  trafo = NULL,
  which_pred = NULL,
  w = NULL,
  breaks = "Sturges",
  right = TRUE,
  discrete_m = 13L,
  outlier_iqr = 2,
  pd_n = 500L,
  seed = NULL,
  ...
)

# S3 method for class 'explainer'
partial_dependence(
  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,
  pd_n = 500L,
  seed = NULL,
  ...
)

# S3 method for class 'H2OModel'
partial_dependence(
  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,
  pd_n = 500L,
  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 should not be binned but rather treated as discrete. The default is 13. Vectorized over v.

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.

pd_n

Size of the data used for calculating partial dependence. The default is 500. For larger data (and w), pd_n rows are randomly sampled. Each variable specified by v uses the same sample. Set to 0 to omit PD calculations.

seed

Optional integer random seed used for:

Partial dependence: select background data if n > pd_n.
Calculating breaks: The bin range is determined without values outside quartiles +- 2 IQR using a sample of <= 9997 observations to calculate quartiles.

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)

partial_dependence(default): Default method.
partial_dependence(ranger): Method for ranger models.
partial_dependence(explainer): Method for DALEX explainers.
partial_dependence(H2OModel): Method for H2O models.

References

Friedman, Jerome H. 2001, Greedy Function Approximation: A Gradient Boosting Machine. Annals of Statistics 29 (5): 1189-1232. doi:10.1214/aos/1013203451.

Examples

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


M2 <- partial_dependence(fit, v = colnames(iris)[-1], data = iris)
plot(M2, share_y = "all")

Arguments

Value

Methods (by class)

References

See also

Examples