Title: A convex pseudolikelihood framework for high dimensional partial correlation estimation with convergence guarantees

Abstract

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear whether corresponding estimators exist or are even computable, or if they actually yield correct partial correlation graphs. We propose a new pseudolikelihood-based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths. In particular, we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms. The objective is then optimized via a coordinate wise approach. The specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees; an important property that cannot be established by using standard results, when the dimension is larger than the sample size, as is often the case in high dimensional applications. These convergence guarantees ensure thatmore » estimators are well defined under very general conditions and are always computable. In addition, the approach yields estimators that have good large sample properties and also respect symmetry. Furthermore, application to simulated and real data, timing comparisons and numerical convergence is demonstrated. We also present a novel unifying framework that places all graphical pseudolikelihood methods as special cases of a more general formulation, leading to important insights.« less

Authors:

Khare, Kshitij ^[1]; Oh, Sang-Yun ^[2]; Rajaratnam, Bala ^[2]

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+ Show Author Affiliations

1. Univ. of Florida, Gainesville, FL (United States)
2. Stanford Univ., CA (United States)

Publication Date:

Fri Sep 26 00:00:00 EDT 2014

Research Org.:

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1523947

Grant/Contract Number:  

AC02-05CH11231; DMS‐1106084; DMS‐0906392; DMS‐CG 1025465; AGS‐1003823, DMS‐1106642, DMS CAREER‐1352656, NSA H98230‐11‐1‐0194; DARPA‐YFA N66001‐111‐4131; SMC‐DBNKY

Resource Type:

Accepted Manuscript

Journal Name:

Journal of the Royal Statistical Society: Series B (Statistical Methodology)

Additional Journal Information:

Journal Name: Journal of the Royal Statistical Society: Series B (Statistical Methodology); Journal Volume: 77; Journal Issue: 4; Journal ID: ISSN 1369-7412

Publisher:

Royal Statistical Society - Wiley

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Sparse inverse covariance estimation; Graphical model selection; Soft thresholding; Partial correlation graph; Convergence guarantee; Generalized pseudo-likelihood; Gene regulatory network