A review of deterministic approximate inference techniques for Bayesian machine learning

A central task of Bayesian machine learning is to infer the posterior distribution of hidden random variables given observations and calculate expectations with respect to this distribution. However, this is often computationally intractable so that people have to seek approximation schemes. Deterministic approximate inference techniques are an alternative of the stochastic approximate inference methods based on numerical sampling, namely Monte Carlo techniques, and during the last 15 years, many advancements in this field have been made. This paper reviews typical deterministic approximate inference techniques, some of which are very recent and need further explorations. With an aim to promote research in deterministic approximate inference, we also attempt to identify open problems that may be helpful for future investigations in this field.