Change point estimation in high dimensional Markov random-field models. (English) Zbl 1373.62260

Roy, Sandipan; Atchadé, Yves; Michailidis, George

J. R. Stat. Soc., Ser. B, Stat. Methodol. 79, No. 4, 1187-1206 (2017).

Summary: The paper investigates a change point estimation problem in the context of high dimensional Markov random-field models. Change points represent a key feature in many dynamically evolving network structures. The change point estimate is obtained by maximizing a profile penalized pseudolikelihood function under a sparsity assumption. We also derive a tight bound for the estimate, up to a logarithmic factor, even in settings where the number of possible edges in the network far exceeds the sample size. The performance of the estimator proposed is evaluated on synthetic data sets and is also used to explore voting patterns in the US Senate in the 1979–2012 period.

MSC:

62H12	Estimation in multivariate analysis
62M40	Random fields; image analysis
62P25	Applications of statistics to social sciences

Keywords:

change point analysis; high-dimensional inference; Markov random fields; network analysis; profile pseudolikelihood