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Related papers: PAC-Bayes under potentially heavy tails

200 papers

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…

Machine Learning · Statistics 2022-12-13 Diederik P Kingma , Max Welling

We study contrastive learning under the PAC learning framework. While a series of recent works have shown statistical results for learning under contrastive loss, based either on the VC-dimension or Rademacher complexity, their algorithms…

Machine Learning · Computer Science 2025-07-08 Jie Shen

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error…

Machine Learning · Statistics 2013-10-23 Emilie Morvant , Sokol Koço , Liva Ralaivola

An agnostic PAC learning algorithm finds a predictor that is competitive with the best predictor in a benchmark hypothesis class, where competitiveness is measured with respect to a given loss function. However, its predictions might be…

Machine Learning · Computer Science 2021-05-24 Guy N Rothblum , Gal Yona

Bayesian neural networks allow us to keep track of uncertainties, for example in top tagging, by learning a tagger output together with an error band. We illustrate the main features of Bayesian versions of established deep-learning…

High Energy Physics - Phenomenology · Physics 2020-01-22 Sven Bollweg , Manuel Haussmann , Gregor Kasieczka , Michel Luchmann , Tilman Plehn , Jennifer Thompson

In meta-learning an agent extracts knowledge from observed tasks, aiming to facilitate learning of novel future tasks. Under the assumption that future tasks are 'related' to previous tasks, the accumulated knowledge should be learned in a…

Machine Learning · Statistics 2019-05-21 Ron Amit , Ron Meir

Existing research has either adapted the Probably Approximately Correct (PAC) Bayesian framework for federated learning (FL) or used information-theoretic PAC-Bayesian bounds while introducing their theorems, but few considering the non-IID…

Machine Learning · Computer Science 2023-09-14 Zihao Zhao , Yang Liu , Wenbo Ding , Xiao-Ping Zhang

Bernstein's condition is a key assumption that guarantees fast rates in machine learning. For example, the Gibbs algorithm with prior $\pi$ has an excess risk in $O(d_{\pi}/n)$, as opposed to the standard $O(\sqrt{d_{\pi}/n})$, where $n$…

Machine Learning · Statistics 2025-03-03 Charles Riou , Pierre Alquier , Badr-Eddine Chérief-Abdellatif

We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm. Classifiers are realized as linearly parametrized deep assignment flows with random initial…

Machine Learning · Statistics 2022-02-21 Bastian Boll , Alexander Zeilmann , Stefania Petra , Christoph Schnörr

The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance…

Machine Learning · Computer Science 2019-06-05 Armin Lederer , Jonas Umlauft , Sandra Hirche

Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where…

Data Structures and Algorithms · Computer Science 2026-03-20 Sitan Chen , Jingqiu Ding , Mahbod Majid , Walter McKelvie

The bias-variance trade-off is a well-known problem in machine learning that only gets more pronounced the less available data there is. In active learning, where labeled data is scarce or difficult to obtain, neglecting this trade-off can…

Large language models often produce confident but incorrect outputs, creating a critical need for reliable uncertainty quantification with formal abstention guarantees. We introduce information-lift certificates that compare model…

Machine Learning · Computer Science 2025-11-20 Sanjeda Akter , Ibne Farabi Shihab , Anuj Sharma

This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an $\ell_0$-penalized maximum likelihood estimator for this…

Machine Learning · Statistics 2025-10-14 Tong Xu , Simge Küçükyavuz , Ali Shojaie , Armeen Taeb

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

Statistics Theory · Mathematics 2019-06-05 Samuel B. Hopkins

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

Statistics Theory · Mathematics 2012-03-02 Theodore P. Hill , Marco Dall'Aglio

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

Methodology · Statistics 2025-08-28 Reza Mohammadi , Marit Schoonhoven , Lucas Vogels , S. Ilker Birbil

We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving…

Machine Learning · Statistics 2021-01-22 Manuel Haussmann , Sebastian Gerwinn , Melih Kandemir

This paper presents four theoretical contributions that improve the usability of risk certificates for neural networks based on PAC-Bayes bounds. First, two bounds on the KL divergence between Bernoulli distributions enable the derivation…

Machine Learning · Computer Science 2025-11-12 Diego García-Pérez , Emilio Parrado-Hernández , John Shawe-Taylor

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…

Methodology · Statistics 2017-08-21 Flávio B Gonçalves , Marcos O. Prates , Victor H. Lachos