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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 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 high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

Data Structures and Algorithms · Computer Science 2019-03-18 Ilias Diakonikolas , Gautam Kamath , Daniel Kane , Jerry Li , Ankur Moitra , Alistair Stewart

Beyond binary classification, learnability can become a logically fragile notion: in EMX, even the class of all finite subsets of $[0,1]$ is learnable in some models of ZFC and not in others. We argue the paradox is operational. The…

Machine Learning · Computer Science 2026-03-03 Jeongho Bang , Kyoungho Cho

In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…

Machine Learning · Computer Science 2025-05-02 Gautam Chandrasekaran , Adam Klivans , Vasilis Kontonis , Raghu Meka , Konstantinos Stavropoulos

Membership queries (MQ) often yield speedups for learning tasks, particularly in the distribution-specific setting. We show that in the \emph{testable learning} model of Rubinfeld and Vasilyan [RV23], membership queries cannot decrease the…

Machine Learning · Computer Science 2025-12-03 Jane Lange , Mingda Qiao

Imitation learning often assumes that demonstrations are close to optimal according to some fixed, but unknown, cost function. However, according to satisficing theory, humans often choose acceptable behavior based on their personal (and…

Machine Learning · Computer Science 2025-05-27 Rushit N. Shah , Nikolaos Agadakos , Synthia Sasulski , Ali Farajzadeh , Sanjiban Choudhury , Brian Ziebart

A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = \mathsf{sign}(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class…

Computational Complexity · Computer Science 2021-11-30 Zander Kelley , Raghu Meka

A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or…

Machine Learning · Computer Science 2016-09-13 Montserrat Hermo , Ana Ozaki

The idea behind the \emph{unsupervised} learning of \emph{disentangled} representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this…

Machine Learning · Computer Science 2020-10-29 Francesco Locatello , Stefan Bauer , Mario Lucic , Gunnar Rätsch , Sylvain Gelly , Bernhard Schölkopf , Olivier Bachem

We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an…

Data Structures and Algorithms · Computer Science 2022-04-19 Vipul Arora , Arnab Bhattacharyya , Noah Fleming , Esty Kelman , Yuichi Yoshida

We study the problem of {\em properly} learning large margin halfspaces in the agnostic PAC model. In more detail, we study the complexity of properly learning $d$-dimensional halfspaces on the unit ball within misclassification error…

Machine Learning · Computer Science 2019-08-30 Ilias Diakonikolas , Daniel M. Kane , Pasin Manurangsi

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

The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…

Machine Learning · Computer Science 2013-11-12 Amit Daniely , Nati Linial , Shai Shalev Shwartz

Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…

Machine Learning · Statistics 2017-09-05 Josip Djolonga , Andreas Krause

We study \emph{learning-to-sample} -- a basic algorithmic task underlying generative modeling -- for Ising models, a standard testbed for algorithmic ideas in both theoretical computer science and machine learning. Given i.i.d. samples of…

Machine Learning · Computer Science 2026-05-26 Andrej Risteski , Thuy-Duong Vuong

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM)…

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

Modeling the spread of social contagions is central to various applications in social computing. In this paper, we study the learnability of the competitive threshold model from a theoretical perspective. We demonstrate how competitive…

Machine Learning · Computer Science 2022-05-10 Yifan Wang , Guangmo Tong

We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…

Data Structures and Algorithms · Computer Science 2017-08-09 Clément L. Canonne , Ilias Diakonikolas , Alistair Stewart