A0380
Title: Regularized estimation and inference of sparse spectral precision matrices
Authors: Navonil Deb - Cornell University (United States) [presenting]
Amy Kuceyeski - Weill Cornell Medicine (United States)
Sumanta Basu - Cornell University (United States)
Abstract: Estimation of the spectral precision matrix, an object of central interest in frequency-domain time series, is a key step in calculating partial coherency and graphical model selection of stationary time series. When the dimension of a time series is large, traditional estimators of spectral precision tend to be severely ill-conditioned, and one needs to resort to suitable regularization strategies involving optimization over complex variables. Existing regularization approaches either separately penalize real and imaginary parts of a complex number or use off-the-shelf optimization routines for complex variables that do not explicitly leverage the underlying sparsity structure of the problem. A complex graphical Lasso (CGLASSO) is proposed as an L1-penalized estimator of a spectral precision matrix based on local Whittle likelihood maximization. Fast pathwise coordinate descent algorithms are developed to implement CGLASSO on large dimensional time series data sets. The algorithm relies on a ring isomorphism between complex and real matrices that maps a number of optimization problems over complex variables to similar optimization problems over real variables. In addition, a framework is proposed for the inference of CGLASSO across different frequencies in high dimensional regimes. Error bounds are calculated for a de-biased CGLASSO estimators and demonstrate asymptotic normality supported with empirical performance.
