Related papers: PAC Learning, VC Dimension, and the Arithmetic Hie…

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…

Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the…

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…

This survey paper gives an overview of various known results on learning classes of Boolean functions in Valiant's Probably Approximately Correct (PAC) learning model and its commonly studied variants.

Delle Rose et al.~(COLT'23) introduced an effective version of the Vapnik-Chervonenkis dimension, and showed that it characterizes improper PAC learning with total computable learners. In this paper, we introduce and study a similar…

We introduce the problem of learning conditional averages in the PAC framework. The learner receives a sample labeled by an unknown target concept from a known concept class, as in standard PAC learning. However, instead of learning the…

Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs…

We show that, in a precise sense, a broad class of feedforward neural networks learn (have finite sample complexity) in the PAC model: every fixed finite feedforward architecture whose layers are definable in an o-minimal structure has…

The Vapnik-Chervonenkis dimension is a combinatorial parameter that reflects the "complexity" of a set of sets (a.k.a. concept classes). It has been introduced by Vapnik and Chervonenkis in their seminal 1971 paper and has since found many…

It is conjectured that the recursive teaching dimension of any finite concept class is upper-bounded by the VC-dimension of this class times a universal constant. In this paper, we confirm this conjecture for two rich families of concept…

Recently, the authors introduced the theory of high-arity PAC learning, which is well-suited for learning graphs, hypergraphs and relational structures. In the same initial work, the authors proved a high-arity analogue of the Fundamental…

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…

We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional…

Strategic classification studies learning settings in which individuals can modify their features, at a cost, in order to influence the classifier's decision. A central question is how the sample complexity of the induced (strategic)…

We are studying the degrees in which a computable structure is relatively computably categoricity, i.e., computably categorcial among all non-computable copies of the structure. Unlike the degrees of computable categoricity we can bound the…

We show a generic reduction from multiclass differentially private PAC learning to binary private PAC learning. We apply this transformation to a recently proposed binary private PAC learner to obtain a private multiclass learner with…

In this short note we observe that the sample complexity of PAC machine learning of various concepts, including learning the maximum (EMX), can be exactly determined when the support of the probability measures considered as models…

For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has…

Classification by neural nets and by tree-based methods are powerful tools of machine learning. There exist interesting visualizations of the inner workings of these and other classifiers. Here we pursue a different goal, which is to…

A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…