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We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification…

Machine Learning · Computer Science 2022-10-21 Felix Biggs , Valentina Zantedeschi , Benjamin Guedj

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of…

Machine Learning · Statistics 2023-10-30 Paul Viallard , Maxime Haddouche , Umut Şimşekli , Benjamin Guedj

This paper presents a series of new results for domain adaptation in the multi-view learning setting. The incorporation of multiple views in the domain adaptation was paid little attention in the previous studies. In this way, we propose an…

Machine Learning · Computer Science 2024-01-03 Mehdi Hennequin , Khalid Benabdeslem , Haytham Elghazel

Variational approximation techniques and inference for stochastic models in machine learning has gained much attention the last years. Especially in the case of Gaussian Processes (GP) and their deep versions, Deep Gaussian Processes…

Statistics Theory · Mathematics 2019-09-24 Roman Föll , Ingo Steinwart

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…

Information Theory · Computer Science 2020-09-10 Fredrik Hellström , Giuseppe Durisi

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…

Machine Learning · Statistics 2022-07-01 Eugenio Clerico , Amitis Shidani , George Deligiannidis , Arnaud Doucet

We explore the family of methods "PAC-Bayes with Backprop" (PBB) to train probabilistic neural networks by minimizing PAC-Bayes bounds. We present two training objectives, one derived from a previously known PAC-Bayes bound, and a second…

Machine Learning · Computer Science 2019-10-07 Omar Rivasplata , Vikram M Tankasali , Csaba Szepesvari

We introduce a data-driven approach to analyze the performance of continuous optimization algorithms using generalization guarantees from statistical learning theory. We study classical and learned optimizers to solve families of parametric…

Optimization and Control · Mathematics 2025-10-07 Rajiv Sambharya , Bartolomeo Stellato

Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good…

Machine Learning · Statistics 2025-02-12 Maxime Haddouche , Paul Viallard , Umut Simsekli , Benjamin Guedj

Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…

Machine Learning · Statistics 2023-11-14 Liam Hodgkinson , Chris van der Heide , Robert Salomone , Fred Roosta , Michael W. Mahoney

PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called…

Machine Learning · Statistics 2026-04-09 Hind Atbir , Farah Cherfaoui , Guillaume Metzler , Emilie Morvant , Paul Viallard

Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative…

Machine Learning · Statistics 2014-11-03 Stefan Wager , William Fithian , Sida Wang , Percy Liang

We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…

Machine Learning · Statistics 2010-07-06 Jean-Yves Audibert , Olivier Catoni

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous…

Machine Learning · Computer Science 2024-05-30 Hossein Zakerinia , Amin Behjati , Christoph H. Lampert

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the…

Machine Learning · Computer Science 2021-12-13 Matias Vera , Leonardo Rey Vega , Pablo Piantanida

We present a general approach, based on exponential inequalities, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds…

Machine Learning · Computer Science 2023-03-10 Fredrik Hellström , Giuseppe Durisi

Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an…

Machine Learning · Computer Science 2020-11-17 Zakaria Mhammedi , Benjamin Guedj , Robert C. Williamson

Generalised Bayesian learning algorithms are increasingly popular in machine learning, due to their PAC generalisation properties and flexibility. The present paper aims at providing a self-contained survey on the resulting PAC-Bayes…

Machine Learning · Statistics 2020-02-06 Benjamin Guedj

We present a PAC-Bayes-style generalization bound which enables the replacement of the KL-divergence with a variety of Integral Probability Metrics (IPM). We provide instances of this bound with the IPM being the total variation metric and…

Machine Learning · Statistics 2023-01-02 Ron Amit , Baruch Epstein , Shay Moran , Ron Meir

We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by…

Machine Learning · Computer Science 2011-05-20 Yevgeny Seldin , François Laviolette , John Shawe-Taylor , Jan Peters , Peter Auer