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Conditional Random Fields via Univariate Exponential Families
Eunho Yang · Pradeep Ravikumar · Genevera I Allen · Zhandong Liu

Sun Dec 08 02:00 PM -- 06:00 PM (PST) @ Harrah's Special Events Center, 2nd Floor
Conditional random fields, which model the distribution of a multivariate response conditioned on a set of covariates using undirected graphs, are widely used in a variety of multivariate prediction applications. Popular instances of this class of models such as categorical-discrete CRFs, Ising CRFs, and conditional Gaussian based CRFs, are not however best suited to the varied types of response variables in many applications, including count-valued responses. We thus introduce a “novel subclass of CRFs”, derived by imposing node-wise conditional distributions of response variables conditioned on the rest of the responses and the covariates as arising from univariate exponential families. This allows us to derive novel multivariate CRFs given any univariate exponential distribution, including the Poisson, negative binomial, and exponential distributions. Also in particular, it addresses the common CRF problem of specifying "feature'' functions determining the interactions between response variables and covariates. We develop a class of tractable penalized $M$-estimators to learn these CRF distributions from data, as well as a unified sparsistency analysis for this general class of CRFs showing exact structure recovery can be achieved with high probability.

Author Information

Eunho Yang (Korea Advanced Institute of Science and Technology; AItrics)
Pradeep Ravikumar (Carnegie Mellon University)
Genevera I Allen (Rice University)
Zhandong Liu (Baylor College of Medicine)

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