10 papers
Sequential testing of conditionally constrained hypotheses
Eugenio Clerico
We explicitly characterise the full class of e-processes for testing conditional non-parametric hypotheses, defined by finitely many conditional constraints. Our main result is a c…
Borel selection of dominating hyperplanes
Eugenio Clerico
We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consid…
Optimal e-values for testing the mean of a bounded random variable against a composite alternative
Sebastian Arnold, Eugenio Clerico
We derive explicitly the e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, thereby providing the first application o…
A simple geometric proof for the characterisation of e-merging functions
Eugenio Clerico
E-values offer a powerful framework for aggregating evidence across different (possibly dependent) statistical experiments. A fundamental question is to identify e-merging function…
Linear Bandits with Non-i.i.d. Noise
Baptiste Abélès, Eugenio Clerico, Hamish Flynn +1
We study the linear stochastic bandit problem, relaxing the standard i.i.d. assumption on the observation noise. As an alternative to this restrictive assumption, we allow the nois…
Confidence Sequences for Generalized Linear Models via Regret Analysis
Eugenio Clerico, Hamish Flynn, Wojciech Kotłowski +1
We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any general…
Optimal e-value testing for properly constrained hypotheses
Eugenio Clerico
Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective stati…
On the optimality of coin-betting for mean estimation
Eugenio Clerico
We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimalit…
Online-to-PAC generalization bounds under graph-mixing dependencies
Baptiste Abélès, Eugenio Clerico, Gergely Neu
Traditional generalization results in statistical learning require a training data set made of independently drawn examples. Most of the recent efforts to relax this independence a…
Generalization bounds for mixing processes via delayed online-to-PAC conversions
Baptiste Abeles, Eugenio Clerico, Gergely Neu
We study the generalization error of statistical learning algorithms in a non-i.i.d. setting, where the training data is sampled from a stationary mixing process. We develop an ana…