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We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose…

We consider the problem of performing linear regression over a stream of $d$-dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without…

Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…

Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while keeping data decentralized. In this paper, we propose a federated sparse sliced inverse…

Given any domain $X\subseteq \mathbb{R}^d$ and a probability measure $\rho$ on $X$, we study the problem of approximating in $L^2(X,\rho)$ a given function $u:X\to\mathbb{R}$, using its noiseless pointwise evaluations at random samples. For…

The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…

Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…

This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the…

Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…

Subsampling is a computationally efficient and scalable method to draw inference in large data settings based on a subset of the data rather than needing to consider the whole dataset. When employing subsampling techniques, a crucial…

In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…

Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension…