This portal has been archived. Explore the next generation of this technology.
Clamping Variables and Approximate Inference
lib:4693b156539e3cd8 (v1.0.0)
Authors: Adrian Weller,Tony Jebara
Where published: NeurIPS 2014 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/5529-clamping-variables-and-approximate-inference
It was recently proved using graph covers (Ruozzi, 2012) that the Bethe partition function is upper bounded by the true partition function for a binary pairwise model that is attractive. Here we provide a new, arguably simpler proof from first principles. We make use of the idea of clamping a variable to a particular value. For an attractive model, we show that summing over the Bethe partition functions for each sub-model obtained after clamping any variable can only raise (and hence improve) the approximation. In fact, we derive a stronger result that may have other useful implications. Repeatedly clamping until we obtain a model with no cycles, where the Bethe approximation is exact, yields the result. We also provide a related lower bound on a broad class of approximate partition functions of general pairwise multi-label models that depends only on the topology. We demonstrate that clamping a few wisely chosen variables can be of practical value by dramatically reducing approximation error.
Where published: NeurIPS 2014 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/5529-clamping-variables-and-approximate-inference
It was recently proved using graph covers (Ruozzi, 2012) that the Bethe partition function is upper bounded by the true partition function for a binary pairwise model that is attractive. Here we provide a new, arguably simpler proof from first principles. We make use of the idea of clamping a variable to a particular value. For an attractive model, we show that summing over the Bethe partition functions for each sub-model obtained after clamping any variable can only raise (and hence improve) the approximation. In fact, we derive a stronger result that may have other useful implications. Repeatedly clamping until we obtain a model with no cycles, where the Bethe approximation is exact, yields the result. We also provide a related lower bound on a broad class of approximate partition functions of general pairwise multi-label models that depends only on the topology. We demonstrate that clamping a few wisely chosen variables can be of practical value by dramatically reducing approximation error.
Relevant initiatives
Related knowledge about this paper
Reproduced results (crowd-benchmarking and competitions)
Artifact and reproducibility checklists
- ACM/cTuning artifact appendix and reproducibility checklist
- NeurIPS reproducibility checklist
- SIGPLAN's checklist for empirical evaluation
- Collective Knowledge (organizing research projects based on FAIR principles)