Related papers: Algorithms and Hardness for Robust Subspace Recove…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Traditional machine learning models focus on achieving good performance on the overall training distribution, but they often underperform on minority groups. Existing methods can improve the worst-group performance, but they can have…

We present an algorithm for solving binary classification problems when the dataset is not fully representative of the problem being solved, and obtaining more data is not possible. It relies on a trained model with loose accuracy…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex…

Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…

With the tremendous success of deep learning in visual tasks, the representations extracted from intermediate layers of learned models, that is, deep features, attract much attention of researchers. Previous empirical analysis shows that…

Finding rare information hidden in a huge amount of data from the Internet is a necessary but complex issue. Many researchers have studied this issue and have found effective methods to detect anomaly data in low dimensional space. However,…

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

The reliability of artificial intelligence (AI) systems in open-world settings depends heavily on their ability to flag out-of-distribution (OOD) inputs unseen during training. Recent advances in large-scale vision-language models (VLMs)…

We consider the problem of learning a linear subspace from data corrupted by outliers. Classical approaches are typically designed for the case in which the subspace dimension is small relative to the ambient dimension. Our approach works…

In list-decodable subspace recovery, the input is a collection of $n$ points $\alpha n$ (for some $\alpha \ll 1/2$) of which are drawn i.i.d. from a distribution $\mathcal{D}$ with a isotropic rank $r$ covariance $\Pi_*$ (the…

Outliers are the points which are different from or inconsistent with the rest of the data. They can be novel, new, abnormal, unusual or noisy information. Outliers are sometimes more interesting than the majority of the data. The main…

In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the…

Outlier recognition is a fundamental problem in data analysis and has attracted a great deal of attention in the past decades. However, most existing methods still suffer from several issues such as high time and space complexities or…

We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data,…

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

In practice, network applications have to deal with failing nodes, malicious attacks, or, somehow, nodes facing highly corrupted data --- generally classified as outliers. This calls for robust, uncomplicated, and efficient methods. We…

We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic…