MOC (Multi-Objective Counterfactual Explanations) for Regression Tasks

Source: R/MOCRegr.R

MOC (Dandl et. al 2020) solves a multi-objective optimization problem to find counterfactuals. The four objectives to minimize are:

  1. dist_target: Distance to desired_prob (classification tasks) or desired_prob (regression tasks).

  2. dist_x_interest: Dissimilarity to x_interest measured by Gower's dissimilarity measure (Gower 1971).

  3. no_changed: Number of feature changes.

  4. dist_train: (Weighted) sum of dissimilarities to the k nearest data points in predictor$data$X.

For optimization, it uses the NSGA II algorithm (Deb et. al 2002) with mixed integer evolutionary strategies (Li et al. 2013) and some tailored adjustments for the counterfactual search (Dandl et al. 2020). Default values for the hyperparameters are based on Dandl et al. 2020.

Details

Several population initialization strategies are available:

  1. random: Feature values of new individuals are sampled from the feature value ranges in predictor$data$X. Some features values are randomly reset to their initial value in x_interest.

  2. sd: Like random, except that the sample ranges of numerical features are limited to one standard deviation from their initial value in x_interest.

  3. icecurve: As in random, feature values are sampled from the feature value ranges in predictor$data$X. Then, however, features are reset with probabilities relative to their importance: the higher the importance of a feature, the higher the probability that its values differ from its value in x_interest. The feature importance is measured using ICE curves (Goldstein et al. 2015).

  4. traindata: Contrary to the other strategies, feature values are drawn from (non-dominated) data points in predictor$data$X; if not enough non-dominated data points are available, remaining individuals are initialized by random sampling. Subsequently, some features values are randomly reset to their initial value in x_interest (as for random).

If use_conditional_mutator is set to TRUE, a conditional mutator samples feature values from the conditional distribution given the other feature values with the help of transformation trees (Hothorn and Zeileis 2017). For details see Dandl et al. 2020.

References

Dandl, S., Molnar, C., Binder, M., and Bischl, B. (2020). "Multi-Objective Counterfactual Explanations". In: Parallel Problem Solving from Nature – PPSN XVI, edited by Thomas Bäck, Mike Preuss, André Deutz, Hao Wang, Carola Doerr, Michael Emmerich, and Heike Trautmann, 448–469, Cham, Springer International Publishing, doi:10.1007/978-3-030-58112-1_31 .

Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). "A fast and elitist multiobjective genetic algorithm: NSGA-II". IEEE transactions on evolutionary computation, 6(2), 182-197.

Goldstein, A., Kapelner, A., Bleich, J., and Pitkin, E. (2015). "Peeking Inside the Black Box: Visualizing Statistical Learning with Plots of Individual Conditional Expectation". Journal of Computational and Graphical Statistics 24 (1): 44–65. doi:10.1080/10618600.2014.907095 .

Gower, J. C. (1971). A general coefficient of similarity and some of its properties. Biometrics, 27, 623–637.

Hothorn, T., Zeileis, A. (2017), "Transformation Forests". Technical Report, arXiv 1701.02110.

Li, Rui, L., Emmerich, M. T. M., Eggermont, J. Bäck, T., Schütz, M., Dijkstra, J., Reiber, J. H. C. (2013). "Mixed Integer Evolution Strategies for Parameter Optimization." Evolutionary Computation 21 (1): 29–64. doi:10.1162/EVCO_a_00059 .

Active bindings

optimizer

(OptimInstanceBatchMultiCrit)
The object used for optimization.

Methods

Public methods

Inherited methods

Method new()

Create a new MOCRegr object.

Usage

MOCRegr$new(
  predictor,
  epsilon = NULL,
  fixed_features = NULL,
  max_changed = NULL,
  mu = 20L,
  termination_crit = "gens",
  n_generations = 175L,
  p_rec = 0.71,
  p_rec_gen = 0.62,
  p_mut = 0.73,
  p_mut_gen = 0.5,
  p_mut_use_orig = 0.4,
  k = 1L,
  weights = NULL,
  lower = NULL,
  upper = NULL,
  init_strategy = "icecurve",
  use_conditional_mutator = FALSE,
  quiet = FALSE,
  distance_function = "gower"
)

Arguments

predictor

(Predictor)
The object (created with iml::Predictor$new()) holding the machine learning model and the data.

epsilon

(numeric(1) | NULL)
If not NULL, candidates whose prediction is farther away from the interval desired_outcome than epsilon are penalized. NULL (default) means no penalization.

fixed_features

(character() | NULL)
Names of features that are not allowed to be changed. NULL (default) allows all features to be changed.

max_changed

(integerish(1) | NULL)
Maximum number of feature changes. NULL (default) allows any number of changes.

mu

(integerish(1))
The population size. Default is 20L.

termination_crit

(character(1)|NULL)
Termination criterion, currently, two criterions are implemented: "gens" (default), which stops after n_generations generations, and "genstag", which stops after the hypervolume did not improve for n_generations generations (the total number of generations is limited to 500).

n_generations

(integerish(1))
The number of generations. Default is 175L.

p_rec

(numeric(1))
Probability with which an individual is selected for recombination. Default is 0.71.

p_rec_gen

(numeric(1))
Probability with which a feature/gene is selected for recombination. Default is 0.62.

p_mut

(numeric(1))
Probability with which an individual is selected for mutation. Default is 0.73.

p_mut_gen

(numeric(1))
Probability with which a feature/gene is selected for mutation. Default is 0.5.

p_mut_use_orig

(numeric(1))
Probability with which a feature/gene is reset to its original value in x_interest after mutation. Default is 0.4.

k

(integerish(1))
The number of data points to use for the forth objective. Default is 1L.

weights

(numeric(1) | numeric(k) | NULL)
The weights used to compute the weighted sum of dissimilarities for the forth objective. It is either a single value or a vector of length k. If it has length k, the i-th element specifies the weight of the i-th closest data point. The values should sum up to 1. NULL (default) means all data points are weighted equally.

lower

(numeric() | NULL)
Vector of minimum values for numeric features. If NULL (default), the element for each numeric feature in lower is taken as its minimum value in predictor$data$X. If not NULL, it should be named with the corresponding feature names.

upper

(numeric() | NULL)
Vector of maximum values for numeric features. If NULL (default), the element for each numeric feature in upper is taken as its maximum value in predictor$data$X. If not NULL, it should be named with the corresponding feature names.

init_strategy

(character(1))
The population initialization strategy. Can be icecurve (default), random, sd or traindata. For more information, see the Details section.

use_conditional_mutator

(logical(1))
Should a conditional mutator be used? The conditional mutator generates plausible feature values based on the values of the other feature. Default is FALSE.

quiet

(logical(1))
Should information about the optimization status be hidden? Default is FALSE.

distance_function

(function() | 'gower' | 'gower_c')
The distance function to be used in the second and fourth objective. Either the name of an already implemented distance function ('gower' or 'gower_c') or a function. If set to 'gower' (default), then Gower's distance (Gower 1971) is used; if set to 'gower_c', a C-based more efficient version of Gower's distance is used. A function must have three arguments x, y, and data and should return a double matrix with nrow(x) rows and maximum nrow(y) columns.

Method plot_statistics()

Plots the evolution of the mean and minimum objective values together with the dominated hypervolume over the generations. All values for a generation are computed based on all non-dominated individuals that emerged until that generation.

Usage

MOCRegr$plot_statistics(centered_obj = TRUE)

Arguments

centered_obj

(logical(1))
Should the objective values be centered? If set to FALSE, each objective value is visualized in a separate plot, since they (usually) have different scales. If set to TRUE (default), they are visualized in a single plot.

Method get_dominated_hv()

Calculates the dominated hypervolume of each generation.

Usage

MOCRegr$get_dominated_hv()

Returns

A data.table with the dominated hypervolume of each generation.

Method plot_search()

Visualizes two selected objective values of all emerged individuals in a scatter plot.

Usage

MOCRegr$plot_search(objectives = c("dist_target", "dist_x_interest"))

Arguments

objectives

(character(2))
The two objectives to be shown in the plot. Possible values are "dist_target", "dist_x_interest, "no_changed", and "dist_train".

Method clone()

The objects of this class are cloneable with this method.

Usage

MOCRegr$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

if (require("randomForest")) {
  # Train a model
  rf = randomForest(mpg ~ ., data = mtcars)
  # Create a predictor object
  predictor = iml::Predictor$new(rf)
  # Find counterfactuals for x_interest
  # \donttest{
  moc_regr = MOCRegr$new(predictor, n_generations = 15L, quiet = TRUE)
  cfactuals = moc_regr$find_counterfactuals(x_interest = mtcars[1L, ], desired_outcome = c(22, 26))
  # Print the counterfactuals
  cfactuals$data
  # Plot evolution of hypervolume and mean and minimum objective values 
  moc_regr$plot_statistics()
  # }
}
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