Let H be a binary-labeled concept class. We prove that can PAC learned by an (approximate) differentially private algorithm if and only it has finite Littlestone dimension. This implies qualitative equivalence between online learnability learnability.

Automated inductive learning is a vital part of machine intelligence and the design of intelligent agents. A useful formalization of inductive learning is the model of PAC-learnability. Nevertheless, the ability to learn every target concept expressible in a given representation, as required in the PAC-learnability model, is highly demanding and leads to many negative results for interesting co...

In this paper we study learning from a logical perspective. We show that there is a strong relationship between a learning strategy, its formal learning framework and its logical represen-tational theory. This relationship enables one to translate learnability results from one theory to another. Moreover if we go from a classical logic theory to a substructural logic theory, we can transform le...

Greater learnability has been offered as an explanation as to why certain properties appear in human languages more frequently than others. Languages with greater learnability are more likely to be accurately transmitted from one generation of learners to the next. We explore whether such a learnability bias is sufficient to result in a property becoming prevalent across languages by formalizin...

We propose to apply a complexity theoretic notion of feasible learnability called "polynomial learnability" to the evaluation of grammatical formalisms for linguistic description. Polynomial learnability was originally defined by Valiant in the context of boolean concept learning and subsequently generalized by Blumer et al. to infinitary domains. We give a clear, intuitive exposition of this n...

We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term of suitable notions of complexity, as well as more recent results that establish the connection between learnability and stability of a learning algorithm.