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Related papers: Learning Functions of Halfspaces

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We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…

Machine Learning · Computer Science 2024-08-22 Michael Sucker , Peter Ochs

We present a PTAS for agnostically learning halfspaces w.r.t. the uniform distribution on the $d$ dimensional sphere. Namely, we show that for every $\mu>0$ there is an algorithm that runs in time $\mathrm{poly}(d,\frac{1}{\epsilon})$, and…

Data Structures and Algorithms · Computer Science 2015-06-26 Amit Daniely

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…

Machine Learning · Computer Science 2023-02-16 Michael Sucker , Peter Ochs

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

Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a…

Machine Learning · Statistics 2026-05-14 Steve Hanneke , Anay Mehrotra , Grigoris Velegkas , Manolis Zampetakis

In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine…

Machine Learning · Computer Science 2025-11-13 Yuxin Bai , Cecelia Shuai , Ashwin De Silva , Siyu Yu , Pratik Chaudhari , Joshua T. Vogelstein

We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…

Data Structures and Algorithms · Computer Science 2026-02-27 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Sihan Liu

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

We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear…

Machine Learning · Computer Science 2013-04-29 Maria Florina Balcan , Philip M. Long

We study the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our main algorithmic result is a polynomial-time PAC learning algorithm for this…

Data Structures and Algorithms · Computer Science 2024-04-02 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Sihan Liu , Nikos Zarifis

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

Data Structures and Algorithms · Computer Science 2015-01-09 Aditya Bhaskara , Ananda Theertha Suresh , Morteza Zadimoghaddam

There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…

Machine Learning · Computer Science 2022-11-22 Ronitt Rubinfeld , Arsen Vasilyan

We introduce a novel technique for verification and model synthesis of sequential programs. Our technique is based on learning a regular model of the set of feasible paths in a program, and testing whether this model contains an incorrect…

Software Engineering · Computer Science 2015-11-04 Yu-Fang Chen , Chiao Hsieh , Ondřej Lengál , Tsung-Ju Lii , Ming-Hsien Tsai , Bow-Yaw Wang , Farn Wang

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

Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…

Computational Complexity · Computer Science 2014-12-09 Mark Bun , Thomas Steinke

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 consider the problem of learning Neural Ordinary Differential Equations (neural ODEs) within the context of Linear Parameter-Varying (LPV) systems in continuous-time. LPV systems contain bilinear systems which are known to be universal…

Machine Learning · Computer Science 2023-07-10 Dániel Rácz , Mihály Petreczky , Bálint Daróczy

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 study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small…

Machine Learning · Computer Science 2018-11-01 Huy L. Nguyen , Lydia Zakynthinou

We introduce a new model of membership query (MQ) learning, where the learning algorithm is restricted to query points that are \emph{close} to random examples drawn from the underlying distribution. The learning model is intermediate…

Machine Learning · Computer Science 2013-04-19 Pranjal Awasthi , Vitaly Feldman , Varun Kanade