skip to content
 

Unbiased approximations of products of expectations

Presented by: 
Anthony Lee University of Warwick
Date: 
Tuesday 4th July 2017 - 09:45 to 10:30
Venue: 
INI Seminar Room 1
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.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons