Energy Model-based Accurate Shapley Value Estimation for Interpretable
  Deep Learning Predictive Modelling
Cheng Lu Jiusun Zeng Yu Xia Jinhui Cai Shihua Luo
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.