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We study the issue of PAC-Bayesian domain adaptation: We want to learn, from a source domain, a majority vote model dedicated to a target one. Our theoretical contribution brings a new perspective by deriving an upper-bound on the target…

Machine Learning · Statistics 2016-07-27 Pascal Germain , Amaury Habrard , François Laviolette , Emilie Morvant

Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some…

Machine Learning · Statistics 2025-03-03 Pierre Alquier

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

We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we…

Machine Learning · Statistics 2019-11-19 Pascal Germain , Amaury Habrard , François Laviolette , Emilie Morvant

We propose an extensive analysis of the behavior of majority votes in binary classification. In particular, we introduce a risk bound for majority votes, called the C-bound, that takes into account the average quality of the voters and…

Machine Learning · Statistics 2015-07-30 Pascal Germain , Alexandre Lacasse , François Laviolette , Mario Marchand , Jean-Francis Roy

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…

Machine Learning · Computer Science 2022-02-07 Wei Huang , Chunrui Liu , Yilan Chen , Tianyu Liu , Richard Yi Da Xu

PAC-Bayes learning is an established framework to both assess the generalisation ability of learning algorithms, and design new learning algorithm by exploiting generalisation bounds as training objectives. Most of the exisiting bounds…

Machine Learning · Statistics 2023-05-31 Maxime Haddouche , Benjamin Guedj

The ability of overparameterized deep networks to generalize well has been linked to the fact that stochastic gradient descent (SGD) finds solutions that lie in flat, wide minima in the training loss -- minima where the output of the…

Machine Learning · Computer Science 2019-06-03 Vaishnavh Nagarajan , J. Zico Kolter

A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…

Machine Learning · Computer Science 2024-03-28 Fredrik Hellström , Giuseppe Durisi , Benjamin Guedj , Maxim Raginsky

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

In the PAC-Bayesian literature, the C-Bound refers to an insightful relation between the risk of a majority vote classifier (under the zero-one loss) and the first two moments of its margin (i.e., the expected margin and the voters'…

Machine Learning · Statistics 2021-09-01 Paul Viallard , Pascal Germain , Amaury Habrard , Emilie Morvant

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A…

Machine Learning · Statistics 2009-01-09 Pierre Alquier

The Bayesian posterior minimizes the "inferential risk" which itself bounds the "predictive risk". This bound is tight when the likelihood and prior are well-specified. However since misspecification induces a gap, the Bayesian posterior…

Machine Learning · Computer Science 2022-05-24 Warren R. Morningstar , Alexander A. Alemi , Joshua V. Dillon

We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution…

Machine Learning · Statistics 2020-12-29 Omar Rivasplata , Ilja Kuzborskij , Csaba Szepesvari , John Shawe-Taylor

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high…

Machine Learning · Computer Science 2023-12-11 Apoorva Sharma , Sushant Veer , Asher Hancock , Heng Yang , Marco Pavone , Anirudha Majumdar

When utilising PAC-Bayes theory for risk certification, it is usually necessary to estimate and bound the Gibbs risk of the PAC-Bayes posterior. Many works in the literature employ a method for this which requires a large number of passes…

Machine Learning · Computer Science 2022-10-21 Felix Biggs

We derive a novel PAC-Bayesian generalization bound for reinforcement learning that explicitly accounts for Markov dependencies in the data, through the chain's mixing time. This contributes to overcoming challenges in obtaining…

Machine Learning · Computer Science 2026-02-10 Abdelkrim Zitouni , Mehdi Hennequin , Juba Agoun , Ryan Horache , Nadia Kabachi , Omar Rivasplata

This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is…

Machine Learning · Computer Science 2013-07-09 David McAllester

Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to…

Machine Learning · Statistics 2026-01-14 Xinping Yi , Gaojie Jin , Xiaowei Huang , Shi Jin

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