Energy Model-based Accurate Shapley Value Estimation for Interpretable Deep Learning Predictive Modelling

As a favorable tool for explainable artificial intelligence (XAI), Shapley value has been widely used to interpret deep learning based predictive models. However, accurate and efficient estimation of Shapley value is a difficult task since the computation load grows exponentially with the increase of input features. Most existing accelerated Shapley value estimation methods have to compromise on estimation accuracy with efficiency. In this article, we present EmSHAP(Energy model-based Shapley value estimation), which can effectively approximate the expectation of Shapley contribution function/deep learning model under arbitrary subset of features given the rest. In order to determine the proposal conditional distribution in the energy model, a gated recurrent unit(GRU) is introduced by mapping the input features onto a hidden space, so that the impact of input feature orderings can be eliminated. In addition, a dynamic masking scheme is proposed to improve the generalization ability. It is proved in Theorems 1, 2 and 3 that EmSHAP achieves tighter error bound than state-of-the-art methods like KernelSHAP and VAEAC, leading to higher estimation accuracy. Finally, case studies on a medical application and an industrial application show that the proposed Shapley value-based explainable framework exhibits enhanced estimation accuracy without compromise on efficiency.