
Learning Loosely Connected Markov Random Fields
We consider the structure learning problem for graphical models that we ...
04/25/2012 ∙ by Rui Wu, et al. ∙ 0 ∙ shareread it

Testing Changes in Communities for the Stochastic Block Model
We introduce the problems of goodnessoffit and twosample testing of t...
11/29/2018 ∙ by Aditya Gangrade, et al. ∙ 0 ∙ shareread it

Structure Learning of Markov Random Fields through GrowShrink Maximum Pseudolikelihood Estimation
Learning the structure of Markov random fields (MRFs) plays an important...
07/03/2018 ∙ by Yuya Takashina, et al. ∙ 0 ∙ shareread it

Estimation of positive definite Mmatrices and structure learning for attractive Gaussian Markov Random fields
Consider a random vector with finite second moments. If its precision ma...
04/26/2014 ∙ by Martin Slawski, et al. ∙ 0 ∙ shareread it

Online Edge Grafting for Efficient MRF Structure Learning
Incremental methods for structure learning of pairwise Markov random fie...
05/25/2017 ∙ by Walid Chaabene, et al. ∙ 0 ∙ shareread it

Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior
In recent years a number of methods have been developed for automaticall...
08/09/2014 ∙ by Yutian Chen, et al. ∙ 0 ∙ shareread it

Support Consistency of Direct SparseChange Learning in Markov Networks
We study the problem of learning sparse structure changes between two Ma...
07/02/2014 ∙ by Song Liu, et al. ∙ 0 ∙ shareread it
Lower Bounds for TwoSample Structural Change Detection in Ising and Gaussian Models
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 tradeoff 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 informationtheoretic lower bounds for reliable change detection over these models. We show that for the Ising model, Ω(d^2/( d)^2 p) samples are required from each dataset to detect even the sparsest possible changes, and that for the Gaussian, Ω( γ^2(p)) samples are required from each dataset to detect change, where γ is the smallest ratio of offdiagonal to diagonal terms in the precision matrices of the distributions. These bounds are compared to the corresponding results in structure learning, and closely match them under mild conditions on the model parameters. Thus, our change detection bounds inherit partial tightness from the structure learning schemes in previous literature, demonstrating that in certain parameter regimes, the naive structure learning based approach to change detection is minimax optimal up to constant factors.
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