Unbiased approximations of products of expectations
40 mins 27 secs,
589.21 MB,
MPEG-4 Video
640x360,
29.97 fps,
44100 Hz,
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Description: |
Lee, A
Tuesday 4th July 2017 - 09:45 to 10:30 |
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Created: | 2017-07-21 12:33 |
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Collection: | Scalable inference; statistical, algorithmic, computational aspects |
Publisher: | Isaac Newton Institute |
Copyright: | Lee, A |
Language: | eng (English) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
Abstract: | I will describe recent work with Simone Tiberi (Zurich) and Giacomo Zanella (Bocconi), on the unbiased approximation of a product of n expectations. Such products arise, e.g., as values of the likelihood function in latent variable models, and unbiased approximations can be used in a pseudo-marginal Markov chain to facilitate inference. A straightforward, standard approach consists of approximating each term using an independent average of M i.i.d. random variables and taking the product of these approximations. While simple, this typically requires M to be O(n) so that the total number of random variables required is N = Mn = O(n^2) in order to control the relative variance of the approximation. Using all N random variables to approximate each expectation is less wasteful when producing them is costly, but produces a biased approximation. We propose an alternative to these two approximations that uses most of the N samples to approximate each expectation in such a way that the estimate of the product of expectations is unbiased. We analyze the variance of this approximation and show that it can result in N = O(n) being sufficient for the relative variance to be controlled as n increases. In situations where the cost of simulations dominates overall computational time, and fixing the relative variance, the proposed approximation is almost n times faster than the standard approach to compute. |
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