TechTalks from event: ICML 2011
Bayesian Inference and Probabilistic Models
Estimating the Bayes Point Using Linear Knapsack ProblemsA Bayes Point machine is a binary classifier that approximates the Bayes-optimal classifier by estimating the mean of the posterior distribution of classifier parameters. Past Bayes Point machines have overcome the intractability of this goal by using message passing techniques that approximate the posterior of the classifier parameters as a Gaussian distribution. In this paper, we investigate alternative message passing approaches that do not rely on Gaussian approximation. To make this possible, we introduce a new computational shortcut based on linear multiple-choice knapsack problems that reduces the complexity of computing Bayes Point belief propagation messages from exponential to linear in the number of data features. Empirical tests of our approach show significant improvement in linear classification over both soft-margin SVMs and Expectation Propagation Bayes Point machines for several real-world UCI datasets.
Message Passing Algorithms for the Dirichlet Diffusion TreeWe demonstrate efficient approximate inference for the Dirichlet Diffusion Tree, a Bayesian nonparametric prior over tree structures. Although DDTs provide a powerful and elegant approach for modeling hierarchies they haven't seen much use to date. One problem is the computational cost of MCMC inference. We provide the first deterministic approximate inference methods for DDT models and show excellent performance compared to the MCMC alternative. We present message passing algorithms to approximate the Bayesian model evidence for a specific tree. This is used to drive sequential tree building and greedy search to find optimal tree structures, corresponding to hierarchical clusterings of the data. We demonstrate appropriate observation models for continuous and binary data. The empirical performance of our method is very close to the computationally expensive MCMC alternative on a density estimation problem, and significantly outperforms kernel density estimators.
Variational Inference for Stick-Breaking Beta Process PriorsWe present a variational Bayesian inference algorithm for the stick-breaking construction of the beta process. We derive an alternate representation of the beta process that is amenable to variational inference, and present a bound relating the truncated beta process to its infinite counterpart. We assess performance on two matrix factorization problems, using a non-negative factorization model and a linear-Gaussian model.
Infinite Dynamic Bayesian NetworksWe present the infinite dynamic Bayesian network model (iDBN), a nonparametric, factored state-space model that generalizes dynamic Bayesian networks (DBNs). The iDBN can infer every aspect of a DBN: the number of hidden factors, the number of values each factor can take, and (arbitrarily complex) connections and conditionals between factors and observations. In this way, the iDBN generalizes other nonparametric state space models, which until now generally focused on binary hidden nodes and more restricted connection structures. We show how this new prior allows us to find interesting structure in benchmark tests and on two real-world datasets involving weather data and neural information flow networks.