Description: "Scaling and Generalizing Variational Inference"

Latent variable models have become a key tool for the modern
statistician, letting us express complex assumptions about the hidden
structures that underlie our data. Latent variable models have been
successfully applied in numerous fields including natural language
processing, computer vision, population genetics, and many others.

The central computational problem in latent variable modeling is
posterior inference, the problem of approximating the conditional
distribution of the latent variables given the observations. Inference
is essential to both exploratory and predictive tasks. Modern
inference algorithms have revolutionized Bayesian statistics,
revealing its potential as a usable and general-purpose language for
data analysis.

Bayesian statistics, however, has not yet reached this potential.
First, statisticians and scientists regularly encounter massive data
sets, but existing algorithms do not scale well. Second, most
approximate inference algorithms are not generic; each must be adapted
to the specific model at hand. This requires significant
model-specific analysis, which precludes us from easily exploring a
variety of models.

In this talk I will discuss our recent research on addressing these
two limitations. First I will describe stochastic variational
inference, an approximate inference algorithm for handling massive
data sets. Stochastic inference is easily applied to a large class of
Bayesian models, including topic models, time-series models, factor
models, and Bayesian nonparametric models. Then I will discuss black
box variational inference, a generic algorithm for approximating the
posterior. We can use black box inference on many models with little
model-specific derivation. Together, these algorithms make Bayesian
statistics a flexible and practical tool for modern data analysis.

This is joint work based on these two papers:

M. Hoffman, D. Blei, J. Paisley, and C. Wang. Stochastic variational
inference. Journal of Machine Learning Research, 14:1303-1347.

http://www.cs.princeton.edu/~blei/papers/HoffmanBleiWangPaisley2013.pdf

R. Ranganath, S. Gerrish and D. Blei. Black box variational inference.
Artificial Intelligence and Statistics, 2014.

Description: Title : On some properties of Polya tree posterior distributions

Abstract :
In Bayesian nonparametrics, Polya tree distributions form a flexible class of priors on distributions or density functions. In the problem of density estimation, for certain choices of parameters, Polya trees have been shown to produce asymptotically consistent posterior distributions in a Hellinger sense.

In this talk, after reviewing some general properties of Polya trees, I will show that the previous consistency result can be made much more precise in two directions: first, rates of convergence can be derived and, second, it is possible to characterise the limiting shape of the posterior distribution in a functional sense. We will discuss applications to Donsker-type results on the cumulative distribution function and to the study of functionals of the density.