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Learning Exponential Family Graphical Models with Latent Variables using Regularized Conditional Likelihood

Taeb, Armeen and Shah, Parikshit and Chandrasekaran, Venkat (2020) Learning Exponential Family Graphical Models with Latent Variables using Regularized Conditional Likelihood. . (Unpublished)

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Fitting a graphical model to a collection of random variables given sample observations is a challenging task if the observed variables are influenced by latent variables, which can induce significant confounding statistical dependencies among the observed variables. We present a new convex relaxation framework based on regularized conditional likelihood for latent-variable graphical modeling in which the conditional distribution of the observed variables conditioned on the latent variables is given by an exponential family graphical model. In comparison to previously proposed tractable methods that proceed by characterizing the marginal distribution of the observed variables, our approach is applicable in a broader range of settings as it does not require knowledge about the specific form of distribution of the latent variables and it can be specialized to yield tractable approaches to problems in which the observed data are not well-modeled as Gaussian. We demonstrate the utility and flexibility of our framework via a series of numerical experiments on synthetic as well as real data.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Taeb, Armeen0000-0002-5647-3160
Subject Keywords:convex optimization, equivariant estimators, exponential family PCA, pseudolikelihood, semidefinite programming
Record Number:CaltechAUTHORS:20210120-142503478
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107598
Deposited By: Tony Diaz
Deposited On:20 Jan 2021 23:09
Last Modified:20 Jan 2021 23:09

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