Tutorial "Variational Bayes and Beyond: Foundations of Scalable Bayesian Inference"

This tutorial is part of the Tutorials on Sampling and Variational Inference during the Special Year on Statistical Machine Learning at Columbia University in the City of New York. The tutorial is taking place at Davis Auditorium at 530 West 120th Street in New York, NY, USA. See this link for other tutorials.

Instructor:
  Professor Tamara Broderick
  Email:

Materials and Description

Title: Variational Bayes and Beyond: Foundations of Scalable Bayesian Inference

Abstract: Bayesian methods exhibit a number of desirable properties for modern data analysis---including (1) coherent quantification of uncertainty, (2) a modular modeling framework able to capture complex phenomena, (3) the ability to incorporate prior information from an expert source, and (4) interpretability. In practice, though, Bayesian inference necessitates approximation of a high-dimensional integral, and some traditional algorithms for this purpose can be slow---notably at data scales of current interest. The tutorial will cover the foundations of some modern tools for fast, approximate Bayesian inference at scale. One increasingly popular framework is provided by "variational Bayes" (VB), which formulates Bayesian inference as an optimization problem. We will examine key benefits and pitfalls of using VB in practice, with a focus on the widespread "mean-field variational Bayes" (MFVB) subtype. We will highlight properties that anyone working with VB, from the data analyst to the theoretician, should be aware of. And we will discuss a number of open challenges.

Prerequisites

Basic familiarity with Bayesian data analysis and its goals. Be familiar with the following concepts: priors, likelihoods, posteriors, Bayes Theorem, and conjugacy (for discrete and continuous distributions).