A non-convex framework for structured non-stationary covariance recovery theory and application

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Tsai, Katherine

Contributors dc:contributor

• Koyejo, Oluwasanmi

• machine learning
• structured learning
• non-convex optimization
• non-stationary covariance
• dynamic functional connectivity

Statement dc:rights

• Copyright 2020 Katherine Tsai

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/108461

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/108461