Statistics Seminar: STA 290
Thursday, November 8th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments 3:30pm, prior to seminar in MSB 4110 (Statistics Lounge)
Speaker: Pradeep Ravikumar (University of Texas)
Title: Graphical Models via Generalized Linear Models
Abstract: Undirected graphical models, also known as Markov networks or Markov random fields, such as Gaussian graphical models and Ising models, are widely used in applications across science and engineering. In many settings, however, the data may not follow Gaussian or binomial distributions that are typically assumed in the standard usage of these models. We introduce a new class of graphical models based on generalized linear models (GLM) by assuming that the node-wise conditional distributions arise from exponential families. Our models allow one to estimate networks using a wide class of exponential distributions, such as the Poisson, negative binomial, and exponential, by fitting penalized GLMs to select the neighborhood for each node. Major contributions of our results include rigorous statistical guarantees showing that the neighborhood of graphical models within our general framework can be recovered exactly with high probability. We will discuss some examples of high-throughput genomic networks learned via our GLM graphical models for multinomial and Poisson distributed data.
This is joint work with Eunho Yang, Genevera Allen, and Zhandong Liu.
Joint paper with Doug Miller (UC Davis)