Related papers: Sample Complexity of Agnostic Multiclass Classific…

The classical PAC sample complexity bounds are stated for any Empirical Risk Minimizer (ERM) and contain an extra logarithmic factor $\log(1/{\epsilon})$ which is known to be necessary for ERM in general. It has been recently shown by…

We consider the problem of determining which classes of functions can be tested more efficiently than they can be learned, in the distribution-free sample-based model that corresponds to the standard PAC learning setting. Our main result…

Networked dynamical systems are widely used as formal models of real-world cascading phenomena, such as the spread of diseases and information. Prior research has addressed the problem of learning the behavior of an unknown dynamical system…

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…

Binary classification from positive-only samples is a variant of PAC learning where the learner receives i.i.d. positive samples and aims to learn a classifier with low error. Previous work by Natarajan, Gereb-Graus, and Shvaytser…

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 2008, Kasiviswanathan et al. defined private learning as a combination of PAC learning and differential privacy. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while…

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…

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum…

Contrastive learning has emerged as a powerful paradigm for self-supervised representation learning. This work analyzes the theoretical limits of contrastive learning under nasty noise, where an adversary modifies or replaces training…

We study multiclass classification in the agnostic adversarial online learning setting. As our main result, we prove that any multiclass concept class is agnostically learnable if and only if its Littlestone dimension is finite. This solves…

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…

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…

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…

In this paper we will give a characterization of the learnability of forgiving 0-1 loss functions in the multiclass setting with effectively finite cardinality of the output and label space. To do this, we create a new combinatorial…

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions,…

We consider the long-standing question of finding a parameter of a class of probability distributions that characterizes its PAC learnability. We provide a rather surprising answer - no such parameter exists. Our techniques allow us to show…

Deep neural networks often contain far more parameters than training examples, yet they still manage to generalize well in practice. Classical complexity measures such as VC-dimension or PAC-Bayes bounds usually become vacuous in this…

We initiate the study of tolerant adversarial PAC-learning with respect to metric perturbation sets. In adversarial PAC-learning, an adversary is allowed to replace a test point $x$ with an arbitrary point in a closed ball of radius $r$…

Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose…