An Introduction to Variational Inference

TL;DR

This paper introduces Variational Inference (VI), a fast optimization-based method for approximating complex probability densities, highlighting its principles, advantages, and applications in modern machine learning models like VAEs and GANs.

Contribution

It provides a comprehensive introduction to VI, explaining its core concepts, mathematical foundations, and applications, facilitating future research in the area.

Findings

VI converges faster than classical sampling methods.

VI effectively approximates complex probability densities.

Applications include VAEs and VAE-GANs.

Abstract

Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate complex probability densities. This property allows VI to converge faster than classical methods, such as, Markov Chain Monte Carlo sampling. Conceptually, VI works by choosing a family of probability density functions and then finding the one closest to the actual probability density -- often using the Kullback-Leibler (KL) divergence as the optimization metric. We introduce the Evidence Lower Bound to tractably compute the approximated probability density and we review the ideas behind mean-field variational inference. Finally, we discuss the applications of VI to variational auto-encoders (VAE) and VAE-Generative Adversarial Network (VAE-GAN). With this paper, we aim to explain the concept of VI and assist in future research with this approach.