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We present and analyze an agnostic active learning algorithm that works without keeping a version space. This is unlike all previous approaches where a restricted set of candidate hypotheses is maintained throughout learning, and only…

Machine Learning · Computer Science 2010-06-15 Alina Beygelzimer , Daniel Hsu , John Langford , Tong Zhang

We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…

Machine Learning · Computer Science 2026-02-25 Ilias Diakonikolas , Daniel M. Kane

We investigate approximation guarantees provided by logistic regression for the fundamental problem of agnostic learning of homogeneous halfspaces. Previously, for a certain broad class of "well-behaved" distributions on the examples,…

Machine Learning · Computer Science 2022-02-01 Ziwei Ji , Kwangjun Ahn , Pranjal Awasthi , Satyen Kale , Stefani Karp

We consider the problem of learning the best-fitting single neuron as measured by the expected square loss $\mathbb{E}_{(x,y)\sim \mathcal{D}}[(\sigma(w^\top x)-y)^2]$ over some unknown joint distribution $\mathcal{D}$ by using gradient…

Machine Learning · Computer Science 2020-09-01 Spencer Frei , Yuan Cao , Quanquan Gu

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The…

Machine Learning · Statistics 2024-10-29 Daniel Soudry , Elad Hoffer , Mor Shpigel Nacson , Suriya Gunasekar , Nathan Srebro

In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse,…

Machine Learning · Computer Science 2022-06-02 Jiulong Liu , Zhaoqiang Liu

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

This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common…

Machine Learning · Statistics 2017-03-20 Andrea Locatelli , Alexandra Carpentier , Samory Kpotufe

Consider the supervised learning setting where the goal is to learn to predict labels $\mathbf y$ given points $\mathbf x$ from a distribution. An \textit{omnipredictor} for a class $\mathcal L$ of loss functions and a class $\mathcal C$ of…

Machine Learning · Computer Science 2024-01-29 Parikshit Gopalan , Princewill Okoroafor , Prasad Raghavendra , Abhishek Shetty , Mihir Singhal

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to…

Machine Learning · Computer Science 2019-04-29 Anish Agarwal , Muhammad Jehangir Amjad , Devavrat Shah , Dennis Shen

For some hypothesis classes and input distributions, active agnostic learning needs exponentially fewer samples than passive learning; for other classes and distributions, it offers little to no improvement. The most popular algorithms for…

Machine Learning · Computer Science 2024-05-24 Eric Price , Yihan Zhou

Convergence and convergence rate analyses of adaptive methods, such as Adaptive Moment Estimation (Adam) and its variants, have been widely studied for nonconvex optimization. The analyses are based on assumptions that the expected or…

Machine Learning · Computer Science 2022-06-28 Hideaki Iiduka

We study distribution-free nonparametric regression following a notion of average smoothness initiated by Ashlagi et al. (2021), which measures the "effective" smoothness of a function with respect to an arbitrary unknown underlying…

Machine Learning · Computer Science 2024-02-14 Steve Hanneke , Aryeh Kontorovich , Guy Kornowski

In this short note, we provide a sample complexity lower bound for learning linear predictors with respect to the squared loss. Our focus is on an agnostic setting, where no assumptions are made on the data distribution. This contrasts with…

Machine Learning · Computer Science 2021-11-23 Ohad Shamir

This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results…

Statistics Theory · Mathematics 2024-01-29 Silvia Novo , Germán Aneiros , Philippe Vieu

The recent advancement of foundation models (FMs) has brought about a paradigm shift, revolutionizing various sectors worldwide. The popular optimizers used to train these models are stochastic gradient descent-based algorithms, which face…

Machine Learning · Computer Science 2026-01-06 Shenglong Zhou , Ouya Wang , Ziyan Luo , Yongxu Zhu , Geoffrey Ye Li

The notion of omnipredictors (Gopalan, Kalai, Reingold, Sharan and Wieder ITCS 2021), suggested a new paradigm for loss minimization. Rather than learning a predictor based on a known loss function, omnipredictors can easily be…

Machine Learning · Computer Science 2023-02-17 Lunjia Hu , Inbal Livni-Navon , Omer Reingold , Chutong Yang

M-estimators are ubiquitous in machine learning and statistical learning theory. They are used both for defining prediction strategies and for evaluating their precision. In this paper, we propose the first non-asymptotic "any-time"…

Statistics Theory · Mathematics 2019-05-27 Victor-Emmanuel Brunel , Arnak S. Dalalyan , Nicolas Schreuder

Single index model is a powerful yet simple model, widely used in statistics, machine learning, and other scientific fields. It models the regression function as $g(<a,x>)$, where a is an unknown index vector and x are the features. This…

Statistics Theory · Mathematics 2020-12-08 Zeljko Kereta , Timo Klock , Valeriya Naumova

We study the algorithmic task of learning Boolean disjunctions in the distribution-free agnostic PAC model. The best known agnostic learner for the class of disjunctions over $\{0, 1\}^n$ is the $L_1$-polynomial regression algorithm,…

Machine Learning · Computer Science 2025-04-22 Ilias Diakonikolas , Daniel M. Kane , Lisheng Ren