English
Related papers

Related papers: An Efficient Tester-Learner for Halfspaces

200 papers

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 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 study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Machine Learning · Computer Science 2023-07-18 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Puqian Wang , Nikos Zarifis

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d…

Data Structures and Algorithms · Computer Science 2026-05-28 Sergei Tikhonov , Arsen Vasilyan

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

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 investigate the generalization properties of a self-training algorithm with halfspaces. The approach learns a list of halfspaces iteratively from labeled and unlabeled training data, in which each iteration consists of two steps:…

Machine Learning · Computer Science 2022-02-16 Lies Hadjadj , Massih-Reza Amini , Sana Louhichi , Alexis Deschamps

We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including…

Machine Learning · Computer Science 2020-02-14 Ilias Diakonikolas , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

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 study the problem of PAC learning halfspaces in the reliable agnostic model of Kalai et al. (2012). The reliable PAC model captures learning scenarios where one type of error is costlier than the others. Our main positive result is a new…

Machine Learning · Computer Science 2024-11-19 Ilias Diakonikolas , Lisheng Ren , Nikos Zarifis

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 the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…

Computational Complexity · Computer Science 2016-03-15 Amit Daniely

In this paper we revisit some classic problems on classification under misspecification. In particular, we study the problem of learning halfspaces under Massart noise with rate $\eta$. In a recent work, Diakonikolas, Goulekakis, and Tzamos…

Machine Learning · Computer Science 2023-09-21 Sitan Chen , Frederic Koehler , Ankur Moitra , Morris Yau

We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…

Machine Learning · Computer Science 2023-11-03 Xinyuan Cao , Santosh S. Vempala

We study the problem of agnostically learning halfspaces under the Gaussian distribution. Our main result is the {\em first proper} learning algorithm for this problem whose sample complexity and computational complexity qualitatively match…

Machine Learning · Computer Science 2021-02-11 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

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

Rubinfeld & Vasilyan recently introduced the framework of testable learning as an extension of the classical agnostic model. It relaxes distributional assumptions which are difficult to verify by conditions that can be checked efficiently…

Machine Learning · Computer Science 2024-11-07 Lucas Slot , Stefan Tiegel , Manuel Wiedmer

Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called iterative polynomial filtering and show a number of striking applications for supervised learning with contamination: (1) We…

Machine Learning · Computer Science 2026-01-13 Adam R. Klivans , Konstantinos Stavropoulos , Kevin Tian , Arsen Vasilyan

We show hardness of improperly learning halfspaces in the agnostic model, both in the distribution-independent as well as the distribution-specific setting, based on the assumption that worst-case lattice problems, such as GapSVP or SIVP,…

Machine Learning · Computer Science 2023-02-21 Stefan Tiegel