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A Nonconvex Framework for Structured Dynamic Covariance Recovery
Katherine Tsai · Mladen Kolar · Sanmi Koyejo

Tue Nov 29 02:00 PM -- 04:00 PM (PST) @ Hall J #1001

We propose a flexible, yet interpretable model for high-dimensional data with time-varying second-order statistics, motivated and applied to functional neuroimaging data. Our approach implements the neuroscientific hypothesis of discrete cognitive processes by factorizing covariances into sparse spatial and smooth temporal components. Although this factorization results in parsimony and domain interpretability, the resulting estimation problem is nonconvex. We design a two-stage optimization scheme with a tailored spectral initialization, combined with iteratively refined alternating projected gradient descent. We prove a linear convergence rate up to a nontrivial statistical error for the proposed descent scheme and establish sample complexity guarantees for the estimator. Empirical results using simulated data and brain imaging data illustrate that our approach outperforms existing baselines.

Author Information

Katherine Tsai (University of Illinois at Urbana-Champaign)
Mladen Kolar (U Chicago)
Sanmi Koyejo (Stanford, Google Research)
Sanmi Koyejo

Sanmi Koyejo is an Assistant Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign and a research scientist at Google AI in Accra. Koyejo's research interests are in developing the principles and practice of adaptive and robust machine learning. Additionally, Koyejo focuses on applications to biomedical imaging and neuroscience. Koyejo co-founded the Black in AI organization and currently serves on its board.

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