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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…

Machine Learning · Computer Science 2023-07-25 Pranjal Awasthi , Nika Haghtalab , Eric Zhao

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…

Machine Learning · Computer Science 2025-02-12 Hassan Ashtiani , Vinayak Pathak , Ruth Urner

We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of…

Machine Learning · Computer Science 2025-07-30 Chao Yan

We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…

Machine Learning · Computer Science 2020-07-15 Alessandro Achille , Giovanni Paolini , Glen Mbeng , Stefano Soatto

One of the most studied problems in machine learning is finding reasonable constraints that guarantee the generalization of a learning algorithm. These constraints are usually expressed as some simplicity assumptions on the target. For…

Machine Learning · Computer Science 2020-01-03 Hassan Hafez-Kolahi , Shohreh Kasaei , Mahdiyeh Soleymani-Baghshah

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…

Machine Learning · Computer Science 2020-05-26 Olivier Bousquet , Steve Hanneke , Shay Moran , Nikita Zhivotovskiy

The complexity of visual stimuli plays an important role in many cognitive phenomena, including attention, engagement, memorability, time perception and aesthetic evaluation. Despite its importance, complexity is poorly understood and…

Computer Vision and Pattern Recognition · Computer Science 2024-05-07 Tingke Shen , Surabhi S Nath , Aenne Brielmann , Peter Dayan

We revisit the problem of characterising the complexity of Quantum PAC learning, as introduced by Bshouty and Jackson [SIAM J. Comput. 1998, 28, 1136-1153]. Several quantum advantages have been demonstrated in this setting, however, none…

Quantum Physics · Physics 2023-09-21 Wilfred Salmon , Sergii Strelchuk , Tom Gur

We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Ilya Nemenman

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

We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…

Discrete Mathematics · Computer Science 2023-01-23 Mason DiCicco , Daniel Reichman

It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…

Information Theory · Computer Science 2008-01-28 David J. Galas , Matti Nykter , Gregory W. Carter , Nathan D. Price , Ilya Shmulevich

We introduce a new information theoretic measure that we call Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of…

Computational Complexity · Computer Science 2018-12-18 Iordanis Kerenidis , Adi Rosén , Florent Urrutia

This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the…

Machine Learning · Computer Science 2016-09-13 Steve Hanneke

The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct…

Information Theory · Computer Science 2015-03-03 Andreas D. Pape , Kenneth J. Kurtz , Hiroki Sayama

A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and…

Machine Learning · Computer Science 2020-08-31 Rafael Frongillo , Ian A. Kash

While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…

Information Theory · Computer Science 2010-06-18 Charles H. Bennett , Peter Gacs , Ming Li , Paul M. B. Vitanyi , Wojciech H. Zurek

We investigate the Probably Approximately Correct (PAC) property of scenario decision algorithms, which refers to their ability to produce decisions with an arbitrarily low risk of violating unknown safety constraints, provided a sufficient…

Machine Learning · Computer Science 2025-08-28 Guillaume O. Berger , Raphaël M. Jungers

Numerical analysts might be expected to pay close attention to a branch of complexity theory called information-based complexity theory (IBCT), which produces an abundance of impressive results about the quest for approximate solutions to…

Numerical Analysis · Mathematics 2025-10-20 Beresford N. Parlett

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that…

Computer Vision and Pattern Recognition · Computer Science 2024-10-29 Thomas Fel , Louis Bethune , Andrew Kyle Lampinen , Thomas Serre , Katherine Hermann