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This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…

Machine Learning · Statistics 2021-03-03 Jie Shen , Chicheng Zhang

The problem of learning $t$-term DNF formulas (for $t = O(1)$) has been studied extensively in the PAC model since its introduction by Valiant (STOC 1984). A $t$-term DNF can be efficiently learnt using a $t$-term DNF only if $t = 1$ i.e.,…

Computational Complexity · Computer Science 2019-11-18 Suprovat Ghoshal , Rishi Saket

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…

Machine Learning · Computer Science 2022-11-28 Aravind Gollakota , Adam R. Klivans , Pravesh K. Kothari

$ \newcommand{\Z}{\mathbb{Z}} \newcommand{\eps}{\varepsilon} \newcommand{\cc}[1]{\mathsf{#1}} \newcommand{\NP}{\cc{NP}} \newcommand{\problem}[1]{\mathrm{#1}} \newcommand{\BDD}{\problem{BDD}} $Bounded Distance Decoding $\BDD_{p,\alpha}$ is…

Computational Complexity · Computer Science 2020-03-19 Huck Bennett , Chris Peikert

Learning intersections of halfspaces is a central problem in Computational Learning Theory. Even for just two halfspaces, it remains a major open question whether learning is possible in polynomial time with respect to the margin $\gamma$…

Machine Learning · Computer Science 2025-11-18 Ilias Diakonikolas , Mingchen Ma , Lisheng Ren , Christos Tzamos

It has been a long-standing problem to efficiently learn a halfspace using as few labels as possible in the presence of noise. In this work, we propose an efficient Perceptron-based algorithm for actively learning homogeneous halfspaces…

Machine Learning · Computer Science 2017-11-07 Songbai Yan , Chicheng Zhang

This paper investigates the phenomenon of benign overfitting in binary classification problems with heavy-tailed input distributions, extending the analysis of maximum margin classifiers to $\alpha$ sub-exponential distributions ($\alpha…

Machine Learning · Computer Science 2024-10-17 Kota Okudo , Kei Kobayashi

We study active learning of homogeneous $s$-sparse halfspaces in $\mathbb{R}^d$ under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most $\eta$ for a parameter $\eta…

Machine Learning · Computer Science 2021-08-16 Chicheng Zhang , Jie Shen , Pranjal Awasthi

Using the recently developed framework of [Daniely et al, 2014], we show that under a natural assumption on the complexity of refuting random K-SAT formulas, learning DNF formulas is hard. Furthermore, the same assumption implies the…

Machine Learning · Computer Science 2014-11-05 Amit Daniely , Shai Shalev-Shwatz

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

Recent work of Klivans, Stavropoulos, and Vasilyan initiated the study of testable learning with distribution shift (TDS learning), where a learner is given labeled samples from training distribution $\mathcal{D}$, unlabeled samples from…

Data Structures and Algorithms · Computer Science 2024-05-22 Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true…

Machine Learning · Computer Science 2021-06-23 Christoph Dann , Yishay Mansour , Mehryar Mohri , Ayush Sekhari , Karthik Sridharan

We study the problem of PAC learning $\gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample…

Machine Learning · Computer Science 2023-06-29 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Puqian Wang , Nikos Zarifis

We examine the task of locating a target region among those induced by intersections of $n$ halfspaces in $\mathbb{R}^d$. This generic task connects to fundamental machine learning problems, such as training a perceptron and learning a…

Machine Learning · Computer Science 2020-10-27 Akash Kumar , Adish Singla , Yisong Yue , Yuxin Chen

Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…

Data Structures and Algorithms · Computer Science 2019-04-25 Aditya Bhaskara , Aidao Chen , Aidan Perreault , Aravindan Vijayaraghavan

We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…

Computational Geometry · Computer Science 2026-03-20 Alexander Munteanu , Simon Omlor , Jeff M. Phillips

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

Machine Learning · Statistics 2016-11-17 Mohammad Hossein Rohban , Prakash Ishwar , Birant Orten , William C. Karl , Venkatesh Saligrama

Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…

Machine Learning · Computer Science 2025-02-12 Hassan Ashtiani , Vinayak Pathak , Ruth Urner

We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given $2^{\tilde{O}(\sqrt{n}/\varepsilon)}$ uniformly random examples of an unknown function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$, our…

Data Structures and Algorithms · Computer Science 2023-05-25 Jane Lange , Arsen Vasilyan

In recent years the framework of learning from label proportions (LLP) has been gaining importance in machine learning. In this setting, the training examples are aggregated into subsets or bags and only the average label per bag is…

Computational Complexity · Computer Science 2024-03-29 Venkatesan Guruswami , Rishi Saket