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Activity Number: 136 - Recent Advances in Dimension Reduction
Type: Contributed
Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #306728
Title: Matrix-Free Likelihood Methods for Exploratory Factor Analysis with High-Dimensional Gaussian Data
Author(s): Fan Dai* and Somak Dutta and Ranjan Maitra
Companies: Iowa State University and Iowa State University and Iowa State University
Keywords: Profile likelihood; Partial SVD; Lanczos algorithm; L-BFGS-B; fMRI; Suicidal ideation data

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis (EFA) with high-dimensional Gaussian data. By implementing a Lanczos algorithm and a limited-memory quasi-Newton method, we develop a matrix free algorithm (HDFA) which does partial singular value decomposition (partial SVD) for data matrix where number of observations n is typically less than the dimension p and it only requires limited amount of memory during likelihood maximization. We perform simulation study with both the randomly generated models and the data-driven models. Results indicate that HDFA substantially outperforms the EM algorithm in all cases. Furthermore, Our algorithm is applied to fit factor models for a fMRI dataset with suicidal attempters, suicidal nonattempters and a control group.

Authors who are presenting talks have a * after their name.

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