Amortized Variational Inference: A Systematic Review

DOI10.1613/JAIR.1.14258arXiv2209.10888OpenAlexW4387663093MaRDI QIDQ6411576

Sanjana Jain, Ankush Ganguly, Ukrit Watchareeruetai

Publication date: 22 September 2022

Abstract: The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several sampling-based techniques. However, the traditional VI algorithm is not scalable to large data sets and is unable to readily infer out-of-bounds data points without re-running the optimization process. Recent developments in the field, like stochastic-, black box- and amortized-VI, have helped address these issues. Generative modeling tasks nowadays widely make use of amortized VI for its efficiency and scalability, as it utilizes a parameterized function to learn the approximate posterior density parameters. With this paper, we review the mathematical foundations of various VI techniques to form the basis for understanding amortized VI. Additionally, we provide an overview of the recent trends that address several issues of amortized VI, such as the amortization gap, generalization issues, inconsistent representation learning, and posterior collapse. Finally, we analyze alternate divergence measures that improve VI optimization.

Full work available at URL: https://doi.org/10.1613/jair.1.14258

Mathematics Subject Classification ID

Bayesian inference (62F15) Applications of mathematical programming (90C90) Learning and adaptive systems in artificial intelligence (68T05) Stochastic programming (90C15) Probabilistic graphical models (62H22)