English
Related papers

Related papers: Testable Learning of General Halfspaces under Mass…

200 papers

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Machine Learning · Statistics 2017-07-20 Tomoharu Iwata , Zoubin Ghahramani

We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log…

Data Structures and Algorithms · Computer Science 2026-03-10 Josh Alman , Shyamal Patel , Rocco A. Servedio

We say that a classifier is \emph{adversarially robust} to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified…

Data Structures and Algorithms · Computer Science 2025-05-21 Jane Lange , Arsen Vasilyan

We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…

Computational Complexity · Computer Science 2023-11-16 Anindya De , Shivam Nadimpalli , Rocco A. Servedio

In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the…

Machine Learning · Computer Science 2018-01-16 Ankit Pensia , Varun Jog , Po-Ling Loh

We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…

Machine Learning · Computer Science 2025-02-04 Jizhou Huang , Brendan Juba

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show…

Computer Vision and Pattern Recognition · Computer Science 2024-02-20 Randall Balestriero , Yann LeCun

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

Machine Learning · Computer Science 2020-07-23 Hassan Ashtiani , Shai Ben-David , Nick Harvey , Christopher Liaw , Abbas Mehrabian , Yaniv Plan

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…

Machine Learning · Computer Science 2023-05-22 Shiwei Zeng , Jie Shen

Recent advances in deep learning have relied on large, labelled datasets to train high-capacity models. However, collecting large datasets in a time- and cost-efficient manner often results in label noise. We present a method for learning…

Computer Vision and Pattern Recognition · Computer Science 2022-07-07 Ahmet Iscen , Jack Valmadre , Anurag Arnab , Cordelia Schmid

We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \in \mathbb{Z}^+$ and $\varepsilon > 0$, it is NP-hard…

Computational Complexity · Computer Science 2017-07-07 Arnab Bhattacharyya , Suprovat Ghoshal , Rishi Saket

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…

Artificial Intelligence · Computer Science 2021-06-29 Dan Geiger , David Heckerman

Attribute-efficient PAC learning of sparse halfspaces has been a fundamental problem in machine learning theory. In recent years, machine learning algorithms are faced with prevalent data corruptions or even malicious attacks. It is of…

Machine Learning · Computer Science 2026-03-06 Shiwei Zeng , Jie Shen

An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…

Information Theory · Computer Science 2021-11-17 Nir Weinberger

We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of…

Data Structures and Algorithms · Computer Science 2017-11-01 Oded Regev , Aravindan Vijayaraghavan

Several recent works [DHLNSY25, CPPS25a, CPPS25b] have studied a model of property testing of Boolean functions under a \emph{relative-error} criterion. In this model, the distance from a target function $f: \{0,1\}^n \to \{0,1\}$ that is…

Computational Complexity · Computer Science 2026-03-24 Xi Chen , Anindya De , Yizhi Huang , Shivam Nadimpalli , Rocco A. Servedio , Tianqi Yang

Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples…

Computer Vision and Pattern Recognition · Computer Science 2022-12-29 Nicolas Bähler , Majed El Helou , Étienne Objois , Kaan Okumuş , Sabine Süsstrunk

In recent years, there has been growing interest in utilizing modern machine learning techniques to learn heuristic functions for forward search algorithms. Despite this, there has been little theoretical understanding of what they should…

Artificial Intelligence · Computer Science 2025-01-07 Carlos Núñez-Molina , Masataro Asai , Pablo Mesejo , Juan Fernández-Olivares

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…

Machine Learning · Computer Science 2019-03-26 Weihao Kong , Gregory Valiant

We derive and analyze a new, efficient, pool-based active learning algorithm for halfspaces, called ALuMA. Most previous algorithms show exponential improvement in the label complexity assuming that the distribution over the instance space…

Machine Learning · Computer Science 2015-03-19 Alon Gonen , Sivan Sabato , Shai Shalev-Shwartz