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We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…

Machine Learning · Computer Science 2026-03-09 Ben Adcock , Juan M. Cardenas , Nick Dexter

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

Machine Learning · Computer Science 2021-04-23 Tian Tong , Cong Ma , Yuejie Chi

In this paper, we study a simple and generic framework to tackle the problem of learning model parameters when a fraction of the training samples are corrupted. We first make a simple observation: in a variety of such settings, the…

Machine Learning · Computer Science 2019-02-20 Yanyao Shen , Sujay Sanghavi

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

Provably sample-efficient Reinforcement Learning (RL) with rich observations and function approximation has witnessed tremendous recent progress, particularly when the underlying function approximators are linear. In this linear regime,…

Machine Learning · Computer Science 2024-08-09 Alekh Agarwal , Tong Zhang

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

Optimization and Control · Mathematics 2022-11-03 Natasa Krejic , Natasa Krklec Jerinkic , Tijana Ostojic

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for…

Computer Vision and Pattern Recognition · Computer Science 2026-05-14 Victor Sechaud , Jérémy Scanvic , Quentin Barthélemy , Patrice Abry , Julián Tachella

Machine unlearning is motivated by desire for data autonomy: a person can request to have their data's influence removed from deployed models, and those models should be updated as if they were retrained without the person's data. We show…

Machine Learning · Computer Science 2024-05-31 Martin Bertran , Shuai Tang , Michael Kearns , Jamie Morgenstern , Aaron Roth , Zhiwei Steven Wu

The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an…

Machine Learning · Computer Science 2023-08-14 Bingxin Zhou , Yuanhong Jiang , Yu Guang Wang , Jingwei Liang , Junbin Gao , Shirui Pan , Xiaoqun Zhang

While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step…

Machine Learning · Computer Science 2020-02-12 David Brandfonbrener , Joan Bruna

We derived the first sparse recovery guarantees for weighted $\ell_1$ minimization with sparse random matrices and the class of weighted sparse signals, using a weighted versions of the null space property to derive these guarantees. These…

Numerical Analysis · Mathematics 2016-05-10 Bubacarr Bah

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…

Information Theory · Computer Science 2013-10-01 Morteza Mardani , Gonzalo Mateos , Georgios B. Giannakis

We consider the problem of learning an unknown product distribution $X$ over $\{0,1\}^n$ using samples $f(X)$ where $f$ is a \emph{known} transformation function. Each choice of a transformation function $f$ specifies a learning problem in…

Machine Learning · Computer Science 2011-03-04 Constantinos Daskalakis , Ilias Diakonikolas , Rocco A. Servedio

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

Statistics Theory · Mathematics 2009-03-06 Anatoli Iouditski , Arkadii S. Nemirovski

Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model.…

Machine Learning · Statistics 2020-02-13 Ayca Ozcelikkale

An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…

Machine Learning · Computer Science 2022-06-06 Zhenmei Shi , Junyi Wei , Yingyu Liang

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…

Information Theory · Computer Science 2020-01-09 Martin Genzel , Peter Jung

Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…

Machine Learning · Statistics 2010-12-07 Daniel Hsu , Sham M. Kakade , Tong Zhang

We consider the problem of phase retrieval from corrupted magnitude observations. In particular we show that a fixed $x_0 \in \mathbb{R}^n$ can be recovered exactly from corrupted magnitude measurements $|\langle a_i, x_0 \rangle | +…

Information Theory · Computer Science 2016-12-13 Paul Hand , Vladislav Voroninski

We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…

Information Theory · Computer Science 2019-10-31 Simon Foucart , Deanna Needell , Reese Pathak , Yaniv Plan , Mary Wootters