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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

We study the problem of efficient PAC active learning of homogeneous linear classifiers (halfspaces) in $\mathbb{R}^d$, where the goal is to learn a halfspace with low error using as few label queries as possible. Under the extra assumption…

Machine Learning · Computer Science 2018-06-05 Chicheng Zhang

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

We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $\nu$. Our main contribution is a Perceptron-like online…

Machine Learning · Computer Science 2021-06-24 Jie Shen

We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear…

Machine Learning · Computer Science 2018-06-05 Pranjal Awasthi , Maria Florina Balcan , Philip M. Long

We give a computationally-efficient PAC active learning algorithm for $d$-dimensional homogeneous halfspaces that can tolerate Massart noise (Massart and N\'ed\'elec, 2006) and Tsybakov noise (Tsybakov, 2004). Specialized to the…

Machine Learning · Computer Science 2021-08-12 Chicheng Zhang , Yinan Li

We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a…

Machine Learning · Computer Science 2023-03-10 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Sihan Liu , Nikos Zarifis

We study the problem of computationally and label efficient PAC active learning $d$-dimensional halfspaces with Tsybakov Noise~\citep{tsybakov2004optimal} under structured unlabeled data distributions. Inspired…

Machine Learning · Computer Science 2024-07-23 Yinan Li , Chicheng Zhang

We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…

Data Structures and Algorithms · Computer Science 2025-11-11 Gautam Chandrasekaran , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

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

We pose a fundamental question in computational learning theory: can we efficiently test whether a training set satisfies the assumptions of a given noise model? This question has remained unaddressed despite decades of research on learning…

Machine Learning · Computer Science 2026-05-11 Surbhi Goel , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

The goal of active learning is to achieve the same accuracy achievable by passive learning, while using much fewer labels. Exponential savings in terms of label complexity have been proved in very special cases, but fundamental lower bounds…

Machine Learning · Statistics 2026-01-01 Yinglun Zhu , Robert Nowak

With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active…

Machine Learning · Computer Science 2020-01-17 Max Hopkins , Daniel Kane , Shachar Lovett , Gaurav Mahajan

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces under the Gaussian distribution on $R^d$ in the presence of some form of query access. In the classical pool-based active learning model, where the…

Machine Learning · Computer Science 2025-01-03 Ilias Diakonikolas , Daniel M. Kane , Mingchen Ma

We study the learnability of linear separators in $\Re^d$ in the presence of bounded (a.k.a Massart) noise. This is a realistic generalization of the random classification noise model, where the adversary can flip each example $x$ with…

Machine Learning · Computer Science 2015-03-13 Pranjal Awasthi , Maria-Florina Balcan , Nika Haghtalab , Ruth Urner

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal…

Machine Learning · Computer Science 2023-03-14 Aravind Gollakota , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

Deep neural networks have great representation power, but typically require large numbers of training examples. This motivates deep active learning methods that can significantly reduce the amount of labeled training data. Empirical…

Machine Learning · Computer Science 2026-01-01 Yinglun Zhu , Robert Nowak

We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(\mathbf{x}, y) \in \mathbb{R}^N \times \{ \pm 1\}$, where the distribution of $\mathbf{x}$ is…

Machine Learning · Computer Science 2022-07-29 Ilias Diakonikolas , Daniel M. Kane , Pasin Manurangsi , Lisheng Ren

We study efficient PAC learning of homogeneous halfspaces in $\mathbb{R}^d$ in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been…

Machine Learning · Computer Science 2021-10-06 Jie Shen

We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the…

Machine Learning · Computer Science 2014-11-06 Maria Florina Balcan , Vitaly Feldman
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