Related papers: Principal Components and Regularized Estimation of…

Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered when looking for common principal components, for example, and the Flury method is a popular approach. However,…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase…

We study a panel data model with general heterogeneous effects where slopes are allowed to vary across both individuals and over time. The key dimension reduction assumption we employ is that the heterogeneous slopes can be expressed as…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

We propose a new method to impute missing values in mixed datasets. It is based on a principal components method, the factorial analysis for mixed data, which balances the influence of all the variables that are continuous and categorical…

There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…

Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…

We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

We analyze the prediction error of principal component regression (PCR) and prove high probability bounds for the corresponding squared risk conditional on the design. Our first main result shows that PCR performs comparably to the oracle…

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…