  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.
