Support Consistency of Direct Sparse-Change Learning in Markov Networks

2014/07/02 by Song Liu, Taiji Suzuki, Liu, Song +9 · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (stat.ML) #Statistical Methods and Inference #stat.ML

paper · pdf · doi:10.48550/arxiv.1407.0581

Rerun experiments, added a new image change detection experiment. Changed some typos in the proof of Proposition 6 and 11

openalex publication_date 2014/07/02 · arxiv created 2016/04/08 · arxiv updated 2016/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 n_p, n_q, the dimension of data m, and the number of changed edges d. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for n_p = Ω(d² log (m²+m)/(2)) and n_q = Ω(n_p²), with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to min(n_p, n_q) = Ω(d² log (m²+m)/(2)) when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.

Citations

• Laplacian matrices of graphs: a survey
• Relative Density-Ratio Estimation for Robust Distribution Comparison
• Learning Structural Changes of Gaussian Graphical Models in Controlled Experiments

Cited by

• Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination
• Projection Pursuit Density Ratio Estimation
• Zero-Flow Encoders

Related

• Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation
• Learning Sparse Structural Changes in High-dimensional Markov Networks: A Review on Methodologies and Theories
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• Two-sample inference for high-dimensional Markov networks
• MOSAIC: Minimax-Optimal Sparsity-Adaptive Inference for Change Points in Dynamic Networks