English
Related papers

Related papers: Information-Theoretic Bayes Risk Lower Bounds for …

200 papers

We introduce a modified version of the excess risk, which can be used to obtain tighter, fast-rate PAC-Bayesian generalisation bounds. This modified excess risk leverages information about the relative hardness of data examples to reduce…

Machine Learning · Computer Science 2023-01-25 Felix Biggs , Benjamin Guedj

We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this…

Information Theory · Computer Science 2016-12-13 Sinem Unal , Aaron B. Wagner

We study strong universal Bayes-consistency in the realizable setting for learning with general metric losses, extending classical characterizations beyond $0$-$1$ classification (Bousquet et al., 2020; Hanneke et al., 2021) and real-valued…

Machine Learning · Computer Science 2026-05-15 Dan Tsir Cohen , Steve Hanneke , Aryeh Kontorovich

We present a new technique to obtain outer-bounds on the capacity region of networks with ultra low-rate feedback. We establish a connection between the achievable rates in the forward channel and the minimum distortion that can be attained…

Information Theory · Computer Science 2021-05-11 Alireza Vahid

We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…

Statistics Theory · Mathematics 2026-03-06 Ben Adcock , Gregor Maier , Rahul Parhi

We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many…

Information Theory · Computer Science 2014-04-30 Cem Aksoylar , Venkatesh Saligrama

We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and…

Machine Learning · Statistics 2024-08-27 Borja Rodríguez-Gálvez , Ragnar Thobaben , Mikael Skoglund

In this paper, we study the sample complexity lower bounds for the exact recovery of parameters and for a positive excess risk of a feed-forward, fully-connected neural network for binary classification, using information-theoretic tools.…

Machine Learning · Statistics 2020-10-30 Xiaochen Yang , Jean Honorio

Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational power. In this chapter, we provide an introduction to these…

Information Theory · Computer Science 2026-05-11 Abbas El Gamal , Maxim Raginsky

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

Statistics Theory · Mathematics 2008-03-04 Jean-Yves Audibert

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Statistics Theory · Mathematics 2009-09-09 Jean-Yves Audibert

This work invokes the notion of $f$-divergence to introduce a novel upper bound on the Bayes error rate of a general classification task. We show that the proposed bound can be computed by sampling from the output of a parameterized model.…

Machine Learning · Computer Science 2025-01-15 Mohammadreza Tavasoli Naeini , Ali Bereyhi , Morteza Noshad , Ben Liang , Alfred O. Hero

For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random…

Information Theory · Computer Science 2026-02-10 Victoria Kostina

The ground truth used for training image, video, or speech quality prediction models is based on the Mean Opinion Scores (MOS) obtained from subjective experiments. Usually, it is necessary to conduct multiple experiments, mostly with…

Audio and Speech Processing · Electrical Eng. & Systems 2021-12-15 Gabriel Mittag , Saman Zadtootaghaj , Thilo Michael , Babak Naderi , Sebastian Möller

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

Statistics Theory · Mathematics 2023-03-02 Shuo Tang , Gerald LaMountain , Tales Imbiriba , Pau Closas

Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…

Machine Learning · Computer Science 2025-09-23 Sri Satish Krishna Chaitanya Bulusu , Mikko Sillanpää

Previous research on PAC-Bayes learning theory has focused extensively on establishing tight upper bounds for test errors. A recently proposed training procedure called PAC-Bayes training, updates the model toward minimizing these bounds.…

Machine Learning · Statistics 2024-10-22 Xitong Zhang , Avrajit Ghosh , Guangliang Liu , Rongrong Wang

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Information Theory · Computer Science 2016-08-31 Jonathan Scarlett , Volkan Cevher

Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…

Machine Learning · Statistics 2020-12-10 Guillermo Valle-Pérez , Ard A. Louis

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…

Machine Learning · Statistics 2024-12-10 Reuben Adams , John Shawe-Taylor , Benjamin Guedj