This is an up-to-date introduction to and overview of the Minimum Description Length (MDL)
Principle, a theory of inductive inference that can be applied to general problems in …

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 …

We develop a representation of a decision maker's uncertainty based on e-variables. Like
the Bayesian posterior, this e-posterior allows for making predictions against arbitrary loss …

We present new excess risk bounds for general unbounded loss functions including log loss
and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold …

Abstract The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999)
can incorporate knowledge about the learning algorithm and (data) distribution through the …

We consider the problem of estimating the mean of a sequence of random elements $ f
(\theta, X_1) $$,\ldots, $$ f (\theta, X_n) $ where $ f $ is a fixed scalar function …

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 …

We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI)
generalization bounds. We derive conditional MI bounds as an instance, with special choice …

Minimax rates for conditional density estimation via empirical entropy Page 1 The Annals of
Statistics 2023, Vol. 51, No. 2, 762–790 https://doi.org/10.1214/23-AOS2270 © Institute of …