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Koyejo, Oluwasanmi Tsai, Katherine 2020-10-07T20:59:41Z 2020-10-07T20:59:41Z 2020-07-09 2020-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms The student, Katherine Tsai, accepted the attached license on 2020-07-08 at 09:35. The student, Katherine Tsai, submitted this Thesis for approval on 2020-07-08 at 09:37. This Thesis was approved for publication on 2020-07-09 at 08:51. DSpace SAF Submission Ingestion Package generated from Vireo submission #15520 on 2020-10-02 at 15:12:32 Made available in DSpace on 2020-10-07T20:59:41Z (GMT). No. of bitstreams: 2 TSAI-THESIS-2020.pdf: 2757247 bytes, checksum: 93e01a73ac75faea9796f1493382f8dd (MD5) LICENSE.txt: 4211 bytes, checksum: 44e7da8e935a669451a2df55e82f24a5 (MD5) Previous issue date: 2020-07-09 application/pdf http://hdl.handle.net/2142/108461 en Copyright 2020 Katherine Tsai machine learning structured learning non-convex optimization non-stationary covariance dynamic functional connectivity A non-convex framework for structured non-stationary covariance recovery theory and application text Thesis Electrical & Computer Eng Electrical & Computer Engr University of Illinois at Urbana-Champaign Thesis M.S.