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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…

Machine Learning · Computer Science 2011-08-11 Vladimir Pestov

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…

Machine Learning · Statistics 2015-07-27 Cosma Rohilla Shalizi , Aryeh Kontorovich

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning,…

Machine Learning · Computer Science 2024-08-07 Max Hopkins , Daniel M. Kane , Shachar Lovett , Gaurav Mahajan

Bayes nets are extensively used in practice to efficiently represent joint probability distributions over a set of random variables and capture dependency relations. In a seminal paper, Chickering et al. (JMLR 2004) showed that given a…

Machine Learning · Computer Science 2024-08-06 Arnab Bhattacharyya , Davin Choo , Sutanu Gayen , Dimitrios Myrisiotis

Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a…

Data Structures and Algorithms · Computer Science 2023-08-23 Robert Ganian , Liana Khazaliya , Kirill Simonov

This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete…

Machine Learning · Statistics 2015-03-13 Elchanan Mossel , Mesrob I. Ohannessian

Despite extensive research since the community learned about adversarial examples 10 years ago, we still do not know how to train high-accuracy classifiers that are guaranteed to be robust to small perturbations of their inputs. Previous…

Computer Vision and Pattern Recognition · Computer Science 2025-07-18 Bernd Prach , Christoph H. Lampert

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

Machine Learning · Statistics 2023-03-29 Soosan Beheshti , Mahdi Shamsi

Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD)…

Machine Learning · Computer Science 2024-04-09 Zhen Fang , Yixuan Li , Feng Liu , Bo Han , Jie Lu

The fundamental theorem of statistical learning states that binary PAC learning is governed by a single parameter -- the Vapnik-Chervonenkis (VC) dimension -- which determines both learnability and sample complexity. Extending this to…

Machine Learning · Computer Science 2025-11-18 Alon Cohen , Liad Erez , Steve Hanneke , Tomer Koren , Yishay Mansour , Shay Moran , Qian Zhang

In this work we consider the problem of data classification in post-classical settings were the number of training examples consists of mere few data points. We explore the phenomenon and reveal key relationships between dimensionality of…

Machine Learning · Computer Science 2022-04-01 Ivan Y. Tyukin , Oliver Sutton , Alexander N. Gorban

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…

Computational Complexity · Computer Science 2023-02-24 Valentino Delle Rose , Alexander Kozachinskiy , Cristobal Rojas , Tomasz Steifer

We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…

Machine Learning · Computer Science 2024-10-22 Daiwei Chen , Wei-Kai Chang , Pratik Chaudhari

Multi-distribution learning generalizes the classic PAC learning to handle data coming from multiple distributions. Given a set of $k$ data distributions and a hypothesis class of VC dimension $d$, the goal is to learn a hypothesis that…

Machine Learning · Computer Science 2024-01-30 Binghui Peng

As learning difficulty is crucial for machine learning (e.g., difficulty-based weighting learning strategies), previous literature has proposed a number of learning difficulty measures. However, no comprehensive investigation for learning…

Machine Learning · Computer Science 2022-09-20 Weiyao Zhu , Ou Wu , Fengguang Su , Yingjun Deng

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…

Machine Learning · Computer Science 2026-03-02 Sajad Ashkezari

This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…

Optimization and Control · Mathematics 2007-05-23 Pirkko Kuusela , Daniel Ocone , Eduardo D. Sontag

We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model…

Machine Learning · Computer Science 2019-05-30 Alessandro Achille , Glen Mbeng , Stefano Soatto

We consider the Domain Adaptation problem, also known as the covariate shift problem, where the distributions that generate the training and test data differ while retaining the same labeling function. This problem occurs across a large…

Machine Learning · Computer Science 2018-12-18 Artidoro Pagnoni , Stefan Gramatovici , Samuel Liu

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

Machine Learning · Statistics 2023-11-06 Sanjeeb Dash , Soumyadip Ghosh , Joao Goncalves , Mark S. Squillante