dc.contributor.advisor Ravikumar, Pradeep en dc.contributor.committeeMember Dhillon, Inderjit en dc.creator Johnson, Christopher Carroll en dc.date.accessioned 2011-11-04T16:54:37Z en dc.date.accessioned 2017-05-11T22:23:40Z dc.date.available 2011-11-04T16:54:37Z en dc.date.available 2017-05-11T22:23:40Z dc.date.issued 2011-08 en dc.date.submitted August 2011 en dc.identifier.uri http://hdl.handle.net/2152/ETD-UT-2011-08-4331 en dc.description text en dc.description.abstract 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 $n=\Omega(d^2\log(p))$ and a stronger irrepresentability condition. We further support these claims with an empirical comparison of the greedy algorithm to node-wise $\ell_1$-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. en dc.format.mimetype application/pdf en dc.language.iso eng en dc.subject Machine learning en dc.subject Graphical models en dc.subject Markov Random Fields en dc.subject Structure learning en dc.subject Probability en dc.subject Uncertainty en dc.subject Greedy algorithms en dc.title Greedy structure learning of Markov Random Fields en dc.description.department Computer Sciences en dc.type.genre thesis en dc.date.updated 2011-11-04T16:54:45Z en dc.identifier.slug 2152/ETD-UT-2011-08-4331 en
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