Quantifying Statistical Significance of Neural Network Representation-Driven Hypotheses by Selective Inference

In the past few years, various approaches have been developed to explain and interpret deep neural network (DNN) representations, but it has been pointed out that these representations are sometimes unstable and not reproducible. In this paper, we interpret these representations as hypotheses driven by DNN (called DNN-driven hypotheses) and propose a method to quantify the reliability of these hypotheses in statistical hypothesis testing framework. To this end, we introduce Selective Inference (SI) framework, which has received much attention in the past few years as a new statistical inference framework for data-driven hypotheses. The basic idea of SI is to make conditional inferences on the selected hypotheses under the condition that they are selected. In order to use SI framework for DNN representations, we develop a new SI algorithm based on homotopy method which enables us to derive the exact (non-asymptotic) conditional sampling distribution of the DNN-driven hypotheses. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method can successfully control the false positive rate, has decent performance in terms of computational efficiency, and provides good results in practical applications.