Accelerating Stochastic Probabilistic Inference

TL;DR

This paper introduces a second-order stochastic variational inference method that improves convergence rates by utilizing Hessian information, demonstrated through experiments on synthetic and real datasets.

Contribution

It develops a second-order SVI approach by deriving the Hessian and proposing efficient numerical schemes, advancing beyond first-order methods.

Findings

Enhanced convergence speed over first-order SVI methods

Effective on both synthetic and real datasets

Demonstrates improved efficiency and accuracy

Abstract

Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization, following noisy estimates of the natural gradient. However, almost all the state-of-the-art SVI algorithms are based on first-order optimization algorithm and often suffer from poor convergence rate. In this paper, we bridge the gap between second-order methods and stochastic variational inference by proposing a second-order based stochastic variational inference approach. In particular, firstly we derive the Hessian matrix of the variational objective. Then we devise two numerical schemes to implement second-order SVI efficiently. Thorough empirical evaluations are investigated on both synthetic and real dataset to backup both the effectiveness and efficiency of the proposed approach.