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Annealing Between Distributions by Averaging Moments

Banff International Research Station for Mathematical Innovation and Discovery

Many powerful Monte Carlo techniques for estimating partition functions, such as annealed importance sampling (AIS), are based on sampling from a sequence of intermediate distributions which interpolate between a tractable initial distribution and the intractable target distribution. The near-universal practice is to use geometric averages of the initial and target distributions, but alternative paths can perform substantially better. We present a novel sequence of intermediate distributions for exponential families defined by averaging the moments of the initial and target distributions. We analyze the asymptotic performance of both the geometric and moment averages paths and derive an asymptotically optimal piecewise linear schedule. AIS with moment averaging performs well empirically at estimating partition functions of restricted Boltzmann machines (RBMs), which form the building blocks of many deep learning models, including Deep Belief Networks and Deep Boltzmann Machines. Joint work with Roger Grosse and Chris Maddison. References: Annealing between Distributions by Averaging Moments. Roger Grosse, Chris Maddison, and Ruslan Salakhutdinov. In Neural Information Processing Systems (NIPS 27) www.cs.toronto.edu/~rsalakhu/papers/nips2013_moment.pdf

Mathematics; Statistics; Biology and other natural sciences; Applied statistics

video/mp4

Author affiliation: University of Toronto

2014-08-07

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49848

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/