Counterfactuals, serving as one of the emerging type of model interpretations, have recently received attention from both researchers and practitioners. Counterfactual explanations formalize the exploration of ``what-if scenarios, and are an instance of example-based reasoning using a set of hypothetical data samples. Counterfactuals essentially show how the model decision alters with input perturbations. Existing methods for generating counterfactuals are mainly algorithm-based, which are time-inefficient and assume the same counterfactual universe for different queries. To address these limitations, we propose a Model-based Counterfactual Synthesizer (MCS) framework for interpreting machine learning models. We first analyze the model-based counterfactual process and construct a base synthesizer using a conditional generative adversarial net (CGAN). To better approximate the counterfactual universe for those rare queries, we novelly employ the umbrella sampling technique to conduct the MCS framework training. Besides, we also enhance the MCS framework by incorporating the causal dependence among attributes with model inductive bias, and validate its design correctness from the causality identification perspective. Experimental results on several datasets demonstrate the effectiveness as well as efficiency of our proposed MCS framework, and verify the advantages compared with other alternatives.
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