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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 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

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

We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples…

Machine Learning · Computer Science 2026-04-30 Jizhou Huang , Brendan Juba

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Data Structures and Algorithms · Computer Science 2017-11-07 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart

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

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

Machine Learning · Computer Science 2015-03-11 Rong Ge , Qingqing Huang , Sham M. Kakade

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

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on…

Machine Learning · Computer Science 2023-02-14 Ilias Diakonikolas , Daniel M. Kane , Lisheng Ren

We study the problem of PAC learning homogeneous halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, the label of every sample is independently flipped with an adversarially controlled probability that can be…

Machine Learning · Computer Science 2020-10-06 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

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 give tight statistical query (SQ) lower bounds for learnining halfspaces in the presence of Massart noise. In particular, suppose that all labels are corrupted with probability at most $\eta$. We show that for arbitrary $\eta \in…

Machine Learning · Computer Science 2022-01-25 Rajai Nasser , Stefan Tiegel

We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first…

Machine Learning · Computer Science 2017-07-06 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…

Data Structures and Algorithms · Computer Science 2021-07-27 Allen Liu , Ankur Moitra

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

A Forster transform is an operation that turns a distribution into one with good anti-concentration properties. While a Forster transform does not always exist, we show that any distribution can be efficiently decomposed as a disjoint…

Machine Learning · Computer Science 2021-07-13 Ilias Diakonikolas , Daniel M. Kane , Christos Tzamos

We study the efficient learnability of high-dimensional Gaussian mixtures in the outlier-robust setting, where a small constant fraction of the data is adversarially corrupted. We resolve the polynomial learnability of this problem when the…

Data Structures and Algorithms · Computer Science 2020-05-14 Ilias Diakonikolas , Samuel B. Hopkins , Daniel Kane , Sushrut Karmalkar

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

Data Structures and Algorithms · Computer Science 2014-05-20 Constantinos Daskalakis , Gautam Kamath

Understanding noise tolerance of machine learning algorithms is a central quest in learning theory. In this work, we study the problem of computationally efficient PAC learning of halfspaces in the presence of malicious noise, where an…

Machine Learning · Computer Science 2025-02-18 Jie Shen