Related papers: PAC Learning, VC Dimension, and the Arithmetic Hie…
A fundamental result of statistical learnig theory states that a concept class is PAC learnable if and only if it is a uniform Glivenko-Cantelli class if and only if the VC dimension of the class is finite. However, the theorem is only…
We study the problem of computable multiclass learnability within the Probably Approximately Correct (PAC) learning framework of Valiant (1984). In the recently introduced computable PAC (CPAC) learning framework of Agarwal et al. (2020),…
We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental Theorem of Statistical Learning, which characterizes PAC…
In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain…
This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in…
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. The uniform Glivenko--Cantelli property…
We study uniform computability properties of PAC learning using Weihrauch complexity. We focus on closed concept classes, which are either represented by positive, by negative or by full information. Among other results, we prove that…
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…
Blumer et al. (1987, 1989) showed that any concept class that is learnable by Occam algorithms is PAC learnable. Board and Pitt (1990) showed a partial converse of this theorem: for concept classes that are closed under exception lists, any…
We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong…
We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning,…
We extend the theory of PAC learning in a way which allows to model a rich variety of learning tasks where the data satisfy special properties that ease the learning process. For example, tasks where the distance of the data from the…
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…
We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related…
This paper contributes to the study of CPAC learnability -- a computable version of PAC learning -- by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class…
In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There are algorithms that learn a near-optimal policy with high probability using a finite amount of samples…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
The Natarajan dimension is a fundamental tool for characterizing multi-class PAC learnability, generalizing the Vapnik-Chervonenkis (VC) dimension from binary to multi-class classification problems. This work establishes upper bounds on…
The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely…