ﻻ يوجد ملخص باللغة العربية
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates.
We consider high-dimensional measurement errors with high-frequency data. Our focus is on recovering the covariance matrix of the random errors with optimality. In this problem, not all components of the random vector are observed at the same time an
We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nominally involves unobservables, we show how to apply it even where the noise covariance structure is not
We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as if the cova
Risk modeling with EHR data is challenging due to a lack of direct observations on the disease outcome, and the high dimensionality of the candidate predictors. In this paper, we develop a surrogate assisted semi-supervised-learning (SAS) approach to
High-dimensional data models, often with low sample size, abound in many interdisciplinary studies, genomics and large biological systems being most noteworthy. The conventional assumption of multinormality or linearity of regression may not be plaus