Support Consistency of Direct Sparse-Change Learning in Markov Networks

The interactions between covariates may change with learning domains. Discovering such transitions may offer key information helping us transfer our knowledge from one domain to another. We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for successful change detection with respect to the sample size np, nq, the dimension of data m, and the number of changed edges d. More specifically, we prove that the true sparse changes can be consistently identified for np = Ω(d2 log m2 +m 2 ) and nq = Ω(n2 p/d), with an exponentially decaying upper-bound on learning error.

• Type: Journal
• Year: 2015
• Where: AAAI
• Authors: Song Liu, Taiji Suzuki, Masashi Sugiyama
• Keywords: AAAI 2015, Intelligent Agents