Fast and flexible inference of joint distributions from their marginals
Author(s)
Frogner, C; Poggio, T
DownloadPublished version (1.156Mb)
Publisher Policy
Publisher Policy
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.
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2019-01-01Department
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 MachinesJournal
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