Greedy structure learning of Markov Random Fields

Probabilistic graphical models are used in a variety of domains to capture and represent general dependencies in joint probability distributions. In this document we examine the problem of learning the structure of an undirected graphical model, also called a Markov Random Field (MRF), given a set of independent and identically distributed (i.i.d.) samples. Specifically, we introduce an adaptive forward-backward greedy algorithm for learning the structure of a discrete, pairwise MRF given a high dimensional set of i.i.d. samples. The algorithm works by greedily estimating the neighborhood of each node independently through a series of forward and backward steps. By imposing a restricted strong convexity condition on the structure of the learned graph we show that the structure can be fully learned with high probability given $n=\Omega(d\log (p))$ samples where $d$ is the dimension of the graph and $p$ is the number of nodes. This is a significant improvement over existing convex-optimization based algorithms that require a sample complexity of n=\Omega(d²\log(p)) and a stronger irrepresentability condition. We further support these claims with an empirical comparison of the greedy algorithm to node-wise \ell₁-regularized logistic regression as well as provide a real data analysis of the greedy algorithm using the Audioscrobbler music listener dataset. The results of this document provide an additional representation of work submitted by A. Jalali, C. Johnson, and P. Ravikumar to NIPS 2011.

Name thesis:degree_name

Master of Science in Computer Sciences

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Texas at Austin

Year dc:date.issued

2011

Author dc:creator

• Johnson, Christopher Carroll

Advisor dc:contributor.advisor

• Ravikumar, Pradeep

Committee member dc:contributor.committeemember

• Dhillon, Inderjit

• Machine learning
• Graphical models
• Markov Random Fields
• Structure learning
• Probability
• Uncertainty
• Greedy algorithms

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/2152/ETD-UT-2011-08-4331

OAI identifier oai:identifier

oai:repositories.lib.utexas.edu:2152/ETD-UT-2011-08-4331