## Electronic Journal of Statistics

### Estimating networks with jumps

#### Abstract

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.

#### Article information

Source
Electron. J. Statist., Volume 6 (2012), 2069-2106.

Dates
First available in Project Euclid: 2 November 2012

https://projecteuclid.org/euclid.ejs/1351865118

Digital Object Identifier
doi:10.1214/12-EJS739

Mathematical Reviews number (MathSciNet)
MR3020257

Zentralblatt MATH identifier
1295.62032

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

#### Citation

Kolar, Mladen; Xing, Eric P. Estimating networks with jumps. Electron. J. Statist. 6 (2012), 2069--2106. doi:10.1214/12-EJS739. https://projecteuclid.org/euclid.ejs/1351865118

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