Title: Statistically Consistent Saliency Estimation. Abstract: The use of deep learning for a wide range of data problems has increased the need for understanding and diagnosing these models, and deep learning interpretation techniques have become an essential tool for data analysts. Although numerous model interpretation methods have been proposed in recent years, most of these procedures are based on heuristics with little or no theoretical guarantees. In this work, we propose a statistical framework for saliency estimation for black box computer vision models. We build a model-agnostic estimation procedure that is statistically consistent and passes the saliency checks of Adebayo et al. (2018). Our method requires solving a linear program, whose solution can be efficiently computed in polynomial time. Through our theoretical analysis, we establish an upper bound on the number of model evaluations needed to recover the region of importance with high probability, and build a new perturbation scheme for estimation of local gradients that is shown to be more efficient than the commonly used random perturbation schemes. Validity of the new method is demonstrated through sensitivity analysis.
