The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.
High-dimensional Ising model selection using ℓ1-regularized logistic regression
Open accessAbstract
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on ℓ1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results provide sufficient conditions on the triple (n, p, d) and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes n=Ω(d3log p) with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of n=Ω(d2log p) suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.
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Cites
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
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Donoho, D. L., & Elad, M. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0437847100 · Cited by 2,898
High-dimensional graphs and variable selection with the Lasso
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Self-citationThe Dantzig selector: Statistical estimation when p is much larger than n
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Metadata
- Authors
- Ravikumar, P., Wainwright, M. J., & Lafferty, J. D.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2010-06-01
- Volume
- 38
- Issue
- 3
- Pages
- 1287-1319
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2128208871
- Cited by
- 892
- References
- 23
- FWCI
- 43.09
- Type
- journal article
- Language
- en
- Open access
- green
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