Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes

A Deep Gaussian Process (DGP) model is a hierarchical composition of GP models that provides a deep Bayesian nonparametric approach to infer the posterior. Exact Bayesian inference is usually intractable for DGPs, motivating the use of various approximations. We theoretically demonstrate that the traditional alternative of mean-field Gaussian assumptions across the hierarchy leads to lack of expressiveness and efficacy of DGP models, whilst stochastic approximation often incurs a significant computational cost. To address this issue, we propose Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes, where a sampler is obtained from a neural generator through minimizing Regularized Stein Discrepancy in L2 space between the approximate distribution and true posterior. Wherein a minimax problem is obtained and solved by Monte Carlo estimation and subsampling stochastic optimization. We experimentally demonstrate the effectiveness and efficiency of the proposed model, by applying it to a more flexible and wider class of posterior approximations on data ranging in size from hundreds to tens of thousands. By comparison, NOVI is superior to previous methods in both classification and regression.