Fast and flexible inference of joint distributions from their marginals
Name
frogner19a.pdf
Description
Published version
Size
1.16 MB
Format
Adobe PDF
Checksum (MD5)
6ebe1d1bbcbe682ac4f2c73eec30e525
Author(s)
Frogner, C
Poggio, Tomaso A
Date Issued
January 1, 2019
Journal
36th International Conference on Machine Learning, ICML 2019
Citation
Frogner, C and Poggio, T. 2019. "Fast and flexible inference of joint distributions from their marginals." 36th International Conference on Machine Learning, ICML 2019, 2019-June.
Version
Final published version
Abstract
Copyright 2019 by the author(s). Across the social sciences and elsewhere, practitioners frequently have to reason about relationships between random variables, despite lacking joint observations of the variables. This is sometimes called an "ecological" inference; given samples from the marginal distributions of the variables, one attempts to infer their joint distribution. The problem is inherently ill-posed, yet only a few models have been proposed for bringing prior information into the problem, often relying on restrictive or unrealistic assumptions and lacking a unified approach. In this paper, we treat the inference problem generally and propose a unified class of models that encompasses some of those previously proposed while including many new ones. Previous work has relied on either relaxation or approximate inference via MCMC, with the latter known to mix prohibitively slowly for this type of problem. Here we instead give a single exact inference algorithm that works for the entire model class via an efficient fixed point iteration called Dykstra's method. We investigate empirically both the computational cost of our algorithm and the accuracy of the new models on real datasets, showing favorable performance in both cases and illustrating the impact of increased flexibility in modeling enabled by this work.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Center for Brains, Minds, and Machines
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
http://proceedings.mlr.press/v97/frogner19a.html
