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We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes…

Machine Learning · Statistics 2015-07-27 Cosma Rohilla Shalizi , Aryeh Kontorovich

We study the problem of multiclass PAC learning with bandit feedback in the realizable setting. In this framework, there is an unknown data distribution over an instance space $\mathcal{X}$ and a label space $\mathcal{Y}$, as in classical…

Machine Learning · Statistics 2026-05-27 Steve Hanneke , Qinglin Meng , Shay Moran , Amirreza Shaeiri

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

We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…

Logic in Computer Science · Computer Science 2025-05-28 Aaron Anderson , Michael Benedikt

List learning is a variant of supervised classification where the learner outputs multiple plausible labels for each instance rather than just one. We investigate classical principles related to generalization within the context of list…

Machine Learning · Computer Science 2026-03-24 Steve Hanneke , Shay Moran , Tom Waknine

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning,…

Machine Learning · Computer Science 2024-08-07 Max Hopkins , Daniel M. Kane , Shachar Lovett , Gaurav Mahajan

How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…

Machine Learning · Computer Science 2020-11-10 Olivier Bousquet , Steve Hanneke , Shay Moran , Ramon van Handel , Amir Yehudayoff

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…

Artificial Intelligence · Computer Science 2019-06-25 Vaishak Belle , Brendan Juba

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

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world…

Machine Learning · Statistics 2025-07-28 Mian Wei , Somesh Jha , David Page

Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk…

Machine Learning · Computer Science 2025-12-10 Julian Asilis , Siddartha Devic , Shaddin Dughmi , Vatsal Sharan , Shang-Hua Teng

We initiate the study of computability requirements for adversarially robust learning. Adversarially robust PAC-type learnability is by now an established field of research. However, the effects of computability requirements in PAC-type…

Machine Learning · Computer Science 2024-06-17 Pascale Gourdeau , Tosca Lechner , Ruth Urner

We study the problem of learning an adversarially robust predictor to test time attacks in the semi-supervised PAC model. We address the question of how many labeled and unlabeled examples are required to ensure learning. We show that…

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

We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…

Machine Learning · Computer Science 2026-03-02 Sajad Ashkezari

A classical result in learning theory shows the equivalence of PAC learnability of binary hypothesis classes and the finiteness of VC dimension. Extending this to the multiclass setting was an open problem, which was settled in a recent…

Machine Learning · Statistics 2023-03-28 Moses Charikar , Chirag Pabbaraju

Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…

Machine Learning · Computer Science 2008-07-10 David Soloveichik

Replicability, introduced by (Impagliazzo et al. STOC '22), is the notion that algorithms should remain stable under a resampling of their inputs (given access to shared randomness). While a strong and interesting notion of stability, the…

Machine Learning · Computer Science 2026-04-09 Max Hopkins , Russell Impagliazzo , Christopher Ye

This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner…

Machine Learning · Computer Science 2024-07-31 Matthew Harrison-Trainor , Syed Akbari

The Fundamental Theorem of Statistical Learning states that a hypothesis space is PAC learnable if and only if its VC dimension is finite. For the agnostic model of PAC learning, the literature so far presents proofs of this theorem that…

Machine Learning · Computer Science 2025-09-29 Lothar Sebastian Krapp , Laura Wirth

A Machine can only learn if it is biased in some way. Typically the bias is supplied by hand, for example through the choice of an appropriate set of features. However, if the learning machine is embedded within an {\em environment} of…

Machine Learning · Computer Science 2020-03-02 Jonathan Baxter