On nesting Monte Carlo estimators

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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.
Publisher
International Machine Learning Society (IMLS)
Issue Date
2018-07-13
Language
English
Citation

35th International Conference on Machine Learning, ICML 2018, pp.6789 - 6817

URI
http://hdl.handle.net/10203/277514
Appears in Collection
CS-Conference Papers(학술회의논문)
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