Poster
Clamping Variables and Approximate Inference
Adrian Weller · Tony Jebara

Thu Dec 11th 02:00 -- 06:00 PM @ Level 2, room 210D #None
in Poster Session »

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.

Author Information

Adrian Weller (Cambridge, Alan Turing Institute)

Adrian Weller is Programme Director for AI at The Alan Turing Institute, the UK national institute for data science and AI, where he is also a Turing Fellow leading work on safe and ethical AI. He is a Senior Research Fellow in Machine Learning at the University of Cambridge, and at the Leverhulme Centre for the Future of Intelligence where he leads the project on Trust and Transparency. His interests span AI, its commercial applications and helping to ensure beneficial outcomes for society. He serves on several boards including the Centre for Data Ethics and Innovation. Previously, Adrian held senior roles in finance.

Tony Jebara (Spotify)

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