A Nonconvex Framework for Structured Dynamic Covariance Recovery
A Nonconvex Framework for Structured Dynamic Covariance Recovery
复制标题
DOI：
--
复制
发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
Katherine Tsai;M. Kolar;Oluwasanmi Koyejo
中科院分区：
文献类型：
--
作者：
Katherine Tsai;M. Kolar;Oluwasanmi Koyejo
我们提出了一个灵活且可解释的高维数据模型，具有时变二阶统计量，激励并应用于功能神经成像数据。受神经科学文献的启发，我们将协方差分解为稀疏的空间分量和光滑的时间分量。虽然这种分解的结果是简约性和领域可解释性，但所得到的估计问题是非凸的。为此，我们设计了一种两阶段优化方案，其中包括精心定制的光谱初始化，结合迭代改进的交替投影梯度下降。我们证明了所提出的下降方案的线性收敛率达到一个非平凡的统计误差，并建立了估计器的样本复杂度保证。我们进一步量化了多元高斯情况下的统计误差。使用模拟和真实脑成像数据的经验结果表明，我们的方法优于现有的基线。
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.