Nonparametric Bayesian Methods: Models, Algorithms, and Applications

This tutorial took place at the Pontificia Universidad Católica de Chile in Santiago, Chile. See this link for the latest versions and videos of this tutorial.

Part I: Saturday, October 7, 9:00 AM–10:30 AM
Part II: Saturday, October 7, 10:50 AM–12:20 PM
Part III: Saturday, October 7, 12:40 PM–1:50 PM

Instructor:
Professor Tamara Broderick
Email:

Description

This tutorial introduces nonparametric Bayes (BNP) as a tool for modern data science and machine learning. BNP methods are useful in a variety of data analyses---including density estimation without parametric assumptions and clustering models that adaptively determine the number of clusters. We will demonstrate that BNP allows the data analyst to learn more from a data set as the size of the data set grows and see how this feat is accomplished. We will describe popular BNP models such as the Dirichlet process, Chinese restaurant process, Indian buffet process, and hierarchical BNP models---and how they relate to each other.

Materials

README for demos
[Slides for Part I]
- Demo 1 [code]: Beta random variable and random distribution intuition
- Demo 2 [code]: Dirichlet random variable and random distribution intuition
- Demo 3 [code]: K large relative to N intuition; empty components
- Demo 4 [code]: K large relative to N intuition; growth of number of clusters
[Slides for Part II]
- Demo 5 [code]: GEM random distribution intuition
- Demo 6 [code]: An exact DPMM simulator
[Slides for Part III]
- Demo 7 [code]: A CRP mixture model sampler

Prerequisites

Working knowledge of Bayesian data analysis. Know how to use Bayes' Theorem to calculate a posterior for both discrete and continuous parametric distributions. Have a basic knowledge of Markov chain Monte Carlo (especially Gibbs) sampling for posterior approximation.

What we won't cover

Gaussian processes are an important branch of nonparametric Bayesian modeling, but we won't have time to cover them here. We'll be focusing on the discrete, or Poisson point process, side of nonparametric Bayesian inference.