English
Related papers

Related papers: Sample Complexity of Agnostic Multiclass Classific…

200 papers

Estimating the relative importance of each sample in a training set has important practical and theoretical value, such as in importance sampling or curriculum learning. This kind of focus on individual samples invokes the concept of…

Machine Learning · Computer Science 2019-01-09 Seung-Geon Lee , Jaedeok Kim , Hyun-Joo Jung , Yoonsuck Choe

The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…

Methodology · Statistics 2019-03-26 Victor Chen , Matthew M. Dunlop , Omiros Papaspiliopoulos , Andrew M. Stuart

Vapnik-Chervonenkis (VC) theory has so far been unable to explain the small generalization error of overparametrized neural networks. Indeed, existing applications of VC theory to large networks obtain upper bounds on VC dimension that are…

Machine Learning · Statistics 2021-10-07 Yutong Wang , Clayton D. Scott

We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $H$ is learnable with transductive sample complexity $m$ precisely when all of its finite…

Machine Learning · Computer Science 2024-10-31 Julian Asilis , Siddartha Devic , Shaddin Dughmi , Vatsal Sharan , Shang-Hua Teng

We consider a PAC-Bayes type learning rule for binary classification, balancing the training error of a randomized ''posterior'' predictor with its KL divergence to a pre-specified ''prior''. This can be seen as an extension of a modified…

Machine Learning · Statistics 2026-03-25 Xiaohan Zhu , Mesrob I. Ohannessian , Nathan Srebro

Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a…

Data Structures and Algorithms · Computer Science 2023-08-23 Robert Ganian , Liana Khazaliya , Kirill Simonov

Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…

Machine Learning · Computer Science 2025-06-24 Chicheng Zhang , Yihan Zhou

In this paper we study the problem of multiclass classification with a bounded number of different labels $k$, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates…

Machine Learning · Computer Science 2023-02-16 Alkis Kalavasis , Grigoris Velegkas , Amin Karbasi

The sample complexity of learning a Boolean-valued function class is precisely characterized by its Rademacher complexity. This has little bearing, however, on the sample complexity of \emph{efficient} agnostic learning. We introduce…

Machine Learning · Computer Science 2017-12-01 Pravesh K. Kothari , Roi Livni

We investigate the Probably Approximately Correct (PAC) property of scenario decision algorithms, which refers to their ability to produce decisions with an arbitrarily low risk of violating unknown safety constraints, provided a sufficient…

Machine Learning · Computer Science 2025-08-28 Guillaume O. Berger , Raphaël M. Jungers

Meta-learning aims to train models that can generalize to new tasks with limited labeled data by extracting shared features across diverse task datasets. Additionally, it accounts for prediction uncertainty during both training and…

Machine Learning · Computer Science 2025-03-03 Hyungi Lee , Chaeyun Jang , Dongbok Lee , Juho Lee

We study the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass…

Machine Learning · Computer Science 2016-04-19 Amit Daniely , Sivan Sabato , Shai Ben-David , Shai Shalev-Shwartz

A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction…

Machine Learning · Computer Science 2015-07-03 Amos Beimel , Kobbi Nissim , Uri Stemmer

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

Machine Learning · Statistics 2023-03-29 Soosan Beheshti , Mahdi Shamsi

In many applications of relational learning, the available data can be seen as a sample from a larger relational structure (e.g. we may be given a small fragment from some social network). In this paper we are particularly concerned with…

Machine Learning · Computer Science 2018-07-05 Ondrej Kuzelka , Yuyi Wang , Steven Schockaert

Learning distribution families over $\mathbb{R}^d$ is a fundamental problem in unsupervised learning and statistics. A central question in this setting is whether a given family of distributions possesses sufficient structure to be (at…

Machine Learning · Statistics 2025-06-10 Arefe Boushehrian , Amir Najafi

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets,…

Condensed Matter · Physics 2009-10-28 S. Mertens , A. Engel

We study robustness to test-time adversarial attacks in the regression setting with $\ell_p$ losses and arbitrary perturbation sets. We address the question of which function classes are PAC learnable in this setting. We show that classes…

Machine Learning · Computer Science 2024-05-07 Idan Attias , Steve Hanneke

Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…

Machine Learning · Computer Science 2025-11-13 Emanuele Troiani , Yatin Dandi , Leonardo Defilippis , Lenka Zdeborová , Bruno Loureiro , Florent Krzakala

In this work, we initiate a formal study of probably approximately correct (PAC) learning under evasion attacks, where the adversary's goal is to \emph{misclassify} the adversarially perturbed sample point $\widetilde{x}$, i.e.,…

Machine Learning · Computer Science 2019-06-14 Dimitrios I. Diochnos , Saeed Mahloujifar , Mohammad Mahmoody