On Nesting Monte Carlo Estimators
Tom Rainforth · Rob Cornish · Hongseok Yang · andrew warrington · Frank Wood

Fri Jul 13th 06:15 -- 09:00 PM @ Hall B #129

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistical implications of nesting MC estimators, including cases of multiple levels of nesting, and establish the conditions under which they converge. We derive corresponding rates of convergence and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naive nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. We demonstrate the applicability of our work by using our results to develop a new estimator for discrete Bayesian experimental design problems and derive error bounds for a class of variational objectives.

Author Information

Tom Rainforth (University of Oxford)
Rob Cornish (Oxford)
Hongseok Yang (KAIST)
andrew warrington (University of Oxford)
Frank Wood (University of Oxford)

Dr. Wood is an associate professor in the Department of Engineering Science at the University of Oxford. Before that he was an assistant professor of Statistics at Columbia University and a research scientist at the Columbia Center for Computational Learning Systems. He formerly was a postdoctoral fellow of the Gatsby Computational Neuroscience Unit of the University College London. He holds a PhD from Brown University (’07) and BS from Cornell University (’96), both in computer science. Dr. Wood is the original architect of both the Anglican and Probabilistic-C probabilistic programming systems. He conducts AI-driven research at the boundary of probabilistic programming, Bayesian modeling, and Monte Carlo methods. Dr. Wood holds 6 patents, has authored over 50 papers, received the AISTATS best paper award in 2009, and has been awarded faculty research awards from Xerox, Google and Amazon. Prior to his academic career he was a successful entrepreneur having run and sold the content-based image retrieval company ToFish! to AOL/Time Warner and served as CEO of Interfolio.

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