  A wide variety of model explanation approaches have been proposed in recent
years, all guided by very different rationales and heuristics. In this paper,
we take a new route and cast interpretability as a statistical inference
problem. We propose a general deep probabilistic model designed to produce
interpretable predictions. The model parameters can be learned via maximum
likelihood, and the method can be adapted to any predictor network architecture
and any type of prediction problem. Our method is a case of amortized
interpretability models, where a neural network is used as a selector to allow
for fast interpretation at inference time. Several popular interpretability
methods are shown to be particular cases of regularised maximum likelihood for
our general model. We propose new datasets with ground truth selection which
allow for the evaluation of the features importance map. Using these datasets,
we show experimentally that using multiple imputation provides more reasonable
interpretations.
