# A Nonconvex Framework for Structured Dynamic Covariance Recovery

arXiv: https://arxiv.org/abs/2011.05601 · HTML: https://mlsanity.com/paper/2011.05601/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians](https://mlsanity.com/paper/2102.05320/) (2021)
- [High-Dimensional Dynamic Covariance Models with Random Forests](https://mlsanity.com/paper/2505.12444/) (2025)

## Abstract (arXiv)

We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances into sparse spatial and smooth temporal components. While this factorization results in both parsimony and domain interpretability, the resulting estimation problem is nonconvex. To this end, we design a two-stage optimization scheme with a carefully 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. We further quantify the statistical error for the multivariate Gaussian case. Empirical results using simulated and real brain imaging data illustrate that our approach outperforms existing baselines.