Related papers: Attribute-Efficient PAC Learning of Low-Degree Pol…

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…

We study the problem of crowdsourced PAC learning of threshold functions. This is a challenging problem and only recently have query-efficient algorithms been established under the assumption that a noticeable fraction of the workers are…

A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…

We study the problem of PAC learning $\gamma$-margin halfspaces with Massart noise. We propose a simple proper learning algorithm, the Perspectron, that has sample complexity $\widetilde{O}((\epsilon\gamma)^{-2})$ and achieves…

This paper studies offline reinforcement learning with linear function approximation in a setting with decision-theoretic, but not estimation sparsity. The structural restrictions of the data-generating process presume that the transitions…

Major complications arise from the recent increase in the amount of high-dimensional data, including high computational costs and memory requirements. Feature selection, which identifies the most relevant and informative attributes of a…

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

The application that motivates this paper is molecular imaging at the atomic level. When discretized at sub-atomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution…

We consider the problem of exactly learning an $s$-sparse real-valued Boolean polynomial of degree $d$ of the form $f:\{ 0,1\}^n \rightarrow \mathbb{R}$. This problem corresponds to decomposing functions in the AND basis and is known as…

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

We consider the problem of learning an unknown $f$ with a sparse Fourier spectrum in the presence of outlier noise. In particular, the algorithm has access to a noisy oracle for (an unknown) $f$ such that (i) the Fourier spectrum of $f$ is…

Contrastive learning has emerged as a powerful paradigm for self-supervised representation learning. This work analyzes the theoretical limits of contrastive learning under nasty noise, where an adversary modifies or replaces training…

Acquiring accurate labels on large-scale datasets is both time consuming and expensive. To reduce the dependency of deep learning models on learning from clean labeled data, several recent research efforts are focused on learning with noisy…

We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

We consider the well-studied Sparse Fourier transform problem, where one aims to quickly recover an approximately Fourier $k$-sparse vector $\widehat{x} \in \mathbb{C}^{n^d}$ from observing its time domain representation $x$. In the exact…

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major…

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular…