MCCE: Monte Carlo sampling of realistic counterfactual explanations

TL;DR

MCCE addresses the need for explainable AI by producing counterfactual explanations that lie on the data manifold and are actionable and valid. It models the joint distribution of mutable features given immutable features and the decision via an autoregressive generator where conditionals are estimated with decision trees, then samples and post-processes to obtain counterfactuals, explicitly conditioning on the desired decision. The key contributions include the decision-conditioned autoregressive modeling, use of CART-based conditionals to handle mixed data and arbitrary categorical levels, guaranteed immutability for actionable changes, and superior speed and cost performance compared with prior on-manifold methods. Empirical results on four real tabular datasets demonstrate strong accuracy, feasibility, and scalability, with additional discussion of privacy implications and avenues for future extension to non-tabular data and alternative generation strategies.

Abstract

We introduce MCCE: Monte Carlo sampling of valid and realistic Counterfactual Explanations for tabular data, a novel counterfactual explanation method that generates on-manifold, actionable and valid counterfactuals by modeling the joint distribution of the mutable features given the immutable features and the decision. Unlike other on-manifold methods that tend to rely on variational autoencoders and have strict prediction model and data requirements, MCCE handles any type of prediction model and categorical features with more than two levels. MCCE first models the joint distribution of the features and the decision with an autoregressive generative model where the conditionals are estimated using decision trees. Then, it samples a large set of observations from this model, and finally, it removes the samples that do not obey certain criteria. We compare MCCE with a range of state-of-the-art on-manifold counterfactual methods using four well-known data sets and show that MCCE outperforms these methods on all common performance metrics and speed. In particular, including the decision in the modeling process improves the efficiency of the method substantially.

Figures (18)

• Figure 1: MCCE's three steps illustrated on the introductory example with two immutable and two mutable features. Step 1: Fit a decision tree for each mutable feature iteratively on the previously fit features and the decision. Step 2: For each observation/prediction to explain, trace the trees down based on the immutable feature values, decision = 1, and previous sampled values, and then randomly sample a training observation in the leaf nodes and update $\bm{D}_h$. Step 3: Among the sampled rows, find the instance closest to the original vector over the decision boundary.
• Figure 2: Experiment 1: The counterfactuals generated for the same random factual of Adult. The bold values indicate the values that are the same as the original factual values.
• Figure 3: Experiment 2: Average and standard deviation (in parentheses) of performance metrics for counterfactuals generated with MCCE as we vary $K$.
• Figure 4: Histograms for three of the variables in the generated data set (white) with the histograms for the real data superimposed (dark grey). Where the histograms overlap, the blend of of white and dark grey gives a light grey color.
• Figure 5: Correlation matrix for the FICO data set. The areas of the circles are proportional to the absolute value of the corresponding correlation coefficients.