Paper Info
Title
Lower Bounds for Testing Graphical Models: Colorings and Antiferromagnetic Ising Models.
Abstract
We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model M and a sampling oracle for the distribution mu(M*) of an unknown model M*, can we efficiently determine if the two models M and M* are the same? We consider identity testing for both soft-constraint and hard-constraint systems. In particular, we prove hardness results in two prototypical cases, the Ising model and proper colorings, and explore whether identity testing is any easier than structure learning. For the ferromagnetic (attractive) Ising model, Daskalakis et al. (2018) presented a polynomial time algorithm for identity testing. We prove hardness results in the anti-ferromagnetic (repulsive) setting in the same regime of parameters where structure learning is known to require a super-polynomial number of samples. Specifically, for n-vertex graphs of maximum degree d, we prove that if vertical bar beta vertical bar d = omega (log n) (where beta is the inverse temperature parameter), then there is no polynomial running time identity testing algorithm unless RP = NP. In the hard-constraint setting, we present hardness results for identity testing for proper colorings. Our results are based on the presumed hardness of #BIS, the problem of (approximately) counting independent sets in bipartite graphs.
Year
Venue
Keywords
2019
JOURNAL OF MACHINE LEARNING RESEARCH
distribution testing,structure learning,graphical models,Ising model,colorings
DocType
Volume
ISSN
Journal
21
1532-4435
Citations 
PageRank 
References 
0
0.34
0
Authors
5
Name
Order
Citations
PageRank
Ivona Bezakova152.29
Antonio Blanca2149.74
Zongchen Chen326.13
Daniel Stefankovic424328.65
Eric Vigoda574776.55