相关论文: PAC Learning, VC Dimension, and the Arithmetic Hie…

In this work, we aim to characterize the statistical complexity of realizable regression both in the PAC learning setting and the online learning setting. Previous work had established the sufficiency of finiteness of the fat shattering…

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…

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…

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…

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…

In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the…

In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a…

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though…

A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…

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…

We begin this report by describing the Probably Approximately Correct (PAC) model for learning a concept class, consisting of subsets of a domain, and a function class, consisting of functions from the domain to the unit interval. Two…

Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt the classical notion of topological dimension (Lebesgue…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

A seminal result in learning theory characterizes the PAC learnability of binary classes through the Vapnik-Chervonenkis dimension. Extending this characterization to the general multiclass setting has been open since the pioneering works…

The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…

In 1984, Valiant [ 7 ] introduced the Probably Approximately Correct (PAC) learning framework for boolean function classes. Blumer et al. [ 2] extended this model in 1989 by introducing the VC dimension as a tool to characterize the…

We examine categoricity issues for computable algebraic fields. We give a structural criterion for relative computable categoricity of these fields, and use it to construct a field that is computably categorical, but not relatively…

This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…

This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating…