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Elementary Estimators for Graphical Models
Eunho Yang · Aurelie C Lozano · Pradeep Ravikumar

Mon Dec 08 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D #None
We propose a class of closed-form estimators for sparsity-structured graphical models, expressed as exponential family distributions, under high-dimensional settings. Our approach builds on observing the precise manner in which the classical graphical model MLE ``breaks down'' under high-dimensional settings. Our estimator uses a carefully constructed, well-defined and closed-form backward map, and then performs thresholding operations to ensure the desired sparsity structure. We provide a rigorous statistical analysis that shows that surprisingly our simple class of estimators recovers the same asymptotic convergence rates as those of the $\ell_1$-regularized MLEs that are much more difficult to compute. We corroborate this statistical performance, as well as significant computational advantages via simulations of both discrete and Gaussian graphical models.

Author Information

Eunho Yang (IBM Research)
Aurelie C Lozano (IBM Research)
Pradeep Ravikumar (Carnegie Mellon University)

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