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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…
Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…
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…
We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust…
Replicability, introduced by (Impagliazzo et al. STOC '22), is the notion that algorithms should remain stable under a resampling of their inputs (given access to shared randomness). While a strong and interesting notion of stability, the…
We analyse the complexity of learning first-order queries in a model-theoretic framework for supervised learning introduced by (Grohe and Tur\'an, TOCS 2004). Previous research on the complexity of learning in this framework focussed on the…
A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect,…
Accuracy is the most important parameter among few others which defines the effectiveness of a machine learning algorithm. Higher accuracy is always desirable. Now, there is a vast number of well established learning algorithms already…
We provide new statistical guarantees for transfer learning via representation learning--when transfer is achieved by learning a feature representation shared across different tasks. This enables learning on new tasks using far less data…
Learning distribution families over $\mathbb{R}^d$ is a fundamental problem in unsupervised learning and statistics. A central question in this setting is whether a given family of distributions possesses sufficient structure to be (at…
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…
Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…
We study the problem of learning an adversarially robust predictor to test time attacks in the semi-supervised PAC model. We address the question of how many labeled and unlabeled examples are required to ensure learning. We show that…
In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…
In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common…
A central challenge in continual learning is forgetting, the loss of performance on previously learned tasks induced by sequential adaptation to new ones. While forgetting has been extensively studied empirically, rigorous theoretical…
Domain generalization is the problem of machine learning when the training data and the test data come from different data domains. We present a simple theoretical model of learning to generalize across domains in which there is a…
Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient…
Transfer learning assumes classifiers of similar tasks share certain parameter structures. Unfortunately, modern classifiers uses sophisticated feature representations with huge parameter spaces which lead to costly transfer. Under the…
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…