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Interpreting Latent Variables in Factor Models via Convex Optimization

Taeb, Armeen and Chandrasekaran, Venkat (2018) Interpreting Latent Variables in Factor Models via Convex Optimization. Mathematical Programming, 167 (1). pp. 129-154. ISSN 0025-5610. http://resolver.caltech.edu/CaltechAUTHORS:20170614-105229927

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Abstract

Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling approach that addresses this challenge by identifying the effects of (a small number of) latent variables on a set of observed variables. However, the latent variables in a factor model are purely mathematical objects that are derived from the observed phenomena, and they do not have any interpretation associated to them. A natural approach for attributing semantic information to the latent variables in a factor model is to obtain measurements of some additional plausibly useful covariates that may be related to the original set of observed variables, and to associate these auxiliary covariates to the latent variables. In this paper, we describe a systematic approach for identifying such associations. Our method is based on solving computationally tractable convex optimization problems, and it can be viewed as a generalization of the minimum-trace factor analysis procedure for fitting factor models via convex optimization. We analyze the theoretical consistency of our approach in a high-dimensional setting as well as its utility in practice via experimental demonstrations with real data.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s10107-017-1187-7DOIArticle
https://link.springer.com/article/10.1007/s10107-017-1187-7PublisherArticle
https://arxiv.org/abs/1601.00389arXivDiscussion Paper
http://rdcu.be/zFiTPublisherFree ReadCube access
ORCID:
AuthorORCID
Taeb, Armeen0000-0002-5647-3160
Additional Information:© 2017 Springer-Verlag GmbH Germany and Mathematical Optimization Society. Received: 2 December 2015; Accepted: 3 August 2017; First Online: 06 September 2017. The authors were supported in part by NSF Career Award CCF-1350590, by Air Force Office of Scientific Research Grant Nos. FA9550-14-1-0098 and FA9550-16-1-0210, by a Sloan research fellowship, and the Resnick Sustainability Institute at Caltech. Armeen Taeb would like to thank Yong Sheng Soh for many helpful discussions.
Group:Resnick Sustainability Institute
Funders:
Funding AgencyGrant Number
NSFCCF-1350590
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0098
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0210
Alfred P. Sloan FoundationUNSPECIFIED
Resnick Sustainability InstituteUNSPECIFIED
Subject Keywords:Canonical correlations analysis; Factor analysis; Log-determinant optimization; Minimum-trace factor analysis; Nuclear-norm relaxation; Semidefinite programming
Classification Code:MSC: 90C34; 90C47; 90C90; 90C25; 62-07; 62F12; 62H25
Record Number:CaltechAUTHORS:20170614-105229927
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170614-105229927
Official Citation:Taeb, A. & Chandrasekaran, V. Math. Program. (2018) 167: 129. https://doi.org/10.1007/s10107-017-1187-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78206
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:14 Jun 2017 20:44
Last Modified:05 Feb 2018 20:55

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