Lower Bounds for Two-Sample Structural Change Detection in Ising and Gaussian Models

28 Oct 2017Aditya GangradeBobak NazerVenkatesh Saligrama

The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between the sample sizes and the reliability of change detection, measured as a minimax risk, for the important cases of the Ising models and the Gaussian Markov random fields restricted to the models which have network structures with $p$ nodes and degree at most $d$, and obtain information-theoretic lower bounds for reliable change detection over these models... (read more)

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