Search Results for author:
Found 3 papers, 0 papers with code
Tighten after Relax: Minimax-Optimal Sparse PCA in Polynomial Time
In this paper, we propose a two-stage sparse PCA procedure that attains the optimal principal subspace estimator in polynomial time.
Nonconvex Statistical Optimization: Minimax-Optimal Sparse PCA in Polynomial Time
To optimally estimate sparse principal subspaces, we propose a two-stage computational framework named "tighten after relax": Within the 'relax' stage, we approximately solve a convex relaxation of sparse PCA with early stopping to obtain a desired initial estimator; For the 'tighten' stage, we propose a novel algorithm called sparse orthogonal iteration pursuit (SOAP), which iteratively refines the initial estimator by directly solving the underlying nonconvex problem.
A Direct Estimation of High Dimensional Stationary Vector Autoregressions
In addition, we provide thorough experiments on both synthetic and real-world equity data to show that there are empirical advantages of our method over the lasso-type estimators in both parameter estimation and forecasting.
