Information-theoretic limits of selecting binary graphical models in high dimensions
| dc.creator | Santhanam, Narayana | |
| dc.creator | Wainwright, Martin J. | |
| dc.date | 2009-05-16 | |
| dc.date.accessioned | 2026-07-07T13:15:52Z | |
| dc.date.available | 2026-07-07T13:15:52Z | |
| dc.description | The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph selection for binary Markov random fields under high-dimensional scaling, in which the graph size $p$ and the number of edges $k$, and/or the maximal node degree $d$ are allowed to increase to infinity as a function of the sample size $n$. For pairwise binary Markov random fields, we derive both necessary and sufficient conditions for correct graph selection over the class $\mathcal{G}_{p,k}$ of graphs on $p$ vertices with at most $k$ edges, and over the class $\mathcal{G}_{p,d}$ of graphs on $p$ vertices with maximum degree at most $d$. For the class $\mathcal{G}_{p, k}$, we establish the existence of constants $c$ and $c'$ such that if $\numobs < c k \log p$, any method has error probability at least 1/2 uniformly over the family, and we demonstrate a graph decoder that succeeds with high probability uniformly over the family for sample sizes $\numobs > c' k^2 \log p$. Similarly, for the class $\mathcal{G}_{p,d}$, we exhibit constants $c$ and $c'$ such that for $n < c d^2 \log p$, any method fails with probability at least 1/2, and we demonstrate a graph decoder that succeeds with high probability for $n > c' d^3 \log p$. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0905.2639 | |
| dc.identifier | http://arxiv.org/abs/0905.2639 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230610 | |
| dc.subject | Information Theory | |
| dc.subject | Machine Learning | |
| dc.subject | Statistics Theory | |
| dc.title | Information-theoretic limits of selecting binary graphical models in high dimensions | |
| dc.type | text |