Open Access
2012 Estimating networks with jumps
Mladen Kolar, Eric P. Xing
Electron. J. Statist. 6: 2069-2106 (2012). DOI: 10.1214/12-EJS739


We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying data collected over a period of time, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely considered in current literature of structural estimation. In particular, we consider the scenario in which the model evolves in a piece-wise constant fashion. We propose a procedure that estimates the structure of a graphical model by minimizing the temporally smoothed L1 penalized regression, which allows jointly estimating the partition boundaries of the VCVS model and the coefficient of the sparse precision matrix on each block of the partition. A highly scalable proximal gradient method is proposed to solve the resultant convex optimization problem; and the conditions for sparsistent estimation and the convergence rate of both the partition boundaries and the network structure are established for the first time for such estimators.


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Mladen Kolar. Eric P. Xing. "Estimating networks with jumps." Electron. J. Statist. 6 2069 - 2106, 2012.


Published: 2012
First available in Project Euclid: 2 November 2012

zbMATH: 1295.62032
MathSciNet: MR3020257
Digital Object Identifier: 10.1214/12-EJS739

Primary: 62G05
Secondary: 62G20

Keywords: dynamic network models , Gaussian graphical models , network models , structural changes

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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