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Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial regression involving…
We address the statistical and optimization impacts of the classical sketch and Hessian sketch used to approximately solve the Matrix Ridge Regression (MRR) problem. Prior research has quantified the effects of classical sketch on the…
In this paper, we investigate a multivariate multi-response (MVMR) linear regression problem, which contains multiple linear regression models with differently distributed design matrices, and different regression and output vectors. The…
Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems,…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…
Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$,…
In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted…
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
We consider the following oblivious sketching problem: given $\epsilon \in (0,1/3)$ and $n \geq d/\epsilon^2$, design a distribution $\mathcal{D}$ over $\mathbb{R}^{k \times nd}$ and a function $f: \mathbb{R}^k \times \mathbb{R}^{nd}…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Cl\'ement…
Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…
We provide a first systematic treatment of so-called rectangular multispectral perturbation theory. With their paper from 2003, Hochstenbach and Plestenjak ["Backward Error, Condition Numbers, and Pseudospectra for the Multiparameter…