Related papers: Robust Randomized Low-Rank Approximation with Row-…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…

Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…

A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…

As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…

Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented…

Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…

This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…

Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…

We study the linear contextual bandit problem in the presence of adversarial corruption, where the reward at each round is corrupted by an adversary, and the corruption level (i.e., the sum of corruption magnitudes over the horizon) is…

Convolutional neural networks have demonstrated high accuracy on various tasks in recent years. However, they are extremely vulnerable to adversarial examples. For example, imperceptible perturbations added to clean images can cause…

We consider learning in an adversarial environment, where an $\varepsilon$-fraction of samples from a distribution $P$ are arbitrarily modified (global corruptions) and the remaining perturbations have average magnitude bounded by $\rho$…