Machine Learning Meetings and Events
Group Meetings: Group meetings are held Mondays from 11am to Noon (talk starts 11:10am) in D.L. Pratt 290C unless otherwise noted. Meetings are coordinated by Hugo Larochelle.
Tea Talks: Tea talks are held every Wednesday at 4:00pm in D.L. Pratt 290C. Talks should be simple, accessible, and not exceed 15 minutes. Speakers bring snacks, make tea, and provide a copy of the presented paper.
Group Meeting Apr 27, 2009: Cumulative distribution networks: Graphical models for cumulative distribution functions
- Speaker: Jim Huang
- Abstract:
We present the cumulative distribution network (CDN) as a novel graphical model which describes the joint CDF of a set of variables. We will show that the rules for assessing conditional independence in CDNs are unlike those for directed, undirected and factor graphs. We will show that the conditional independence criteria for CDNs defined over continuous variables in fact corresponds to those of bi-directed models for continuous variables. We will then provide both sufficient and necessary conditions for a CDN to have a dual representation as a factor graph with latent variables, so that the joint probability model described by the CDN exhibits the same conditional independence relationships as that of a factor graph with additional latent variables introduced. This will then allow us to construct multivariate extreme value distributions for which both a factor graph and CDN representation exists.
We will then discuss the problem of performing inference under CDNs, which we will show corresponds to computing derivatives of the joint CDF. We will describe a message-passing algorithm for inference in CDNs called the derivative-sum-product algorithm and demonstrate its use on a problem of structured ranking in multiplayer gaming. We will then present a general framework for structured ranking learning in which we are given many observations of partial orderings over many objects to be ranked and we wish to learn to rank these objects whilst accounting for a high degree of dependency between outputs. Results will be presented for applications of structured ranking learning to the problems of document retrieval and regulatory sequence discovery in computational biology. For this class of applications, CDNs provide a graphical structure which includes previous probabilistic models for rank data, such as the Plackett-Luce, Bradley-Terry models.