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Title:A non-convex framework for structured non-stationary covariance recovery theory and application
Author(s):Tsai, Katherine
Advisor(s):Koyejo, Oluwasanmi
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):machine learning
structured learning
non-convex optimization
non-stationary covariance
dynamic functional connectivity
Abstract:Flexible, yet interpretable, models for the second-order temporal structure are needed in scientific analyses of high-dimensional data. The thesis develops a structured time-indexed covariance model for non-stationary time-series data by decomposing them into sparse spatial and temporally smooth components. Traditionally, time-indexed covariance models without structure require a large sample size to be estimable. While the covariances factorization results in both domain interpretability and ease of estimation from the statistical perspective, the resulting optimization problem used to estimate the model components is non-convex. We design an optimization scheme with a carefully tailored spectral initialization, combined with iteratively re ned alternating projected gradient descent. We prove a linear convergence rate for the proposed descent scheme and establish sample complexity guarantees for the estimator. As a motivating example, we consider the neuroscience application of estimation of dynamic brain connectivity. Empirical results using simulated and real brain imaging data illustrate that our approach improves time-varying covariance estimation as compared to baselines.
Issue Date:2020-07-09
Rights Information:Copyright 2020 Katherine Tsai
Date Available in IDEALS:2020-10-07
Date Deposited:2020-08

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