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We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…
Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components…
The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating…
This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…
Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…