On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation

no code implementations • 21 Jun 2023 • Samir M. Perlaza, Iñaki Esnaola, Gaetan Bisson, H. Vincent Poor

The dependence on training data of the Gibbs algorithm (GA) is analytically characterized.

Empirical Risk Minimization with Relative Entropy Regularization

no code implementations • 12 Nov 2022 • Samir M. Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, Stefano Rini

Among these properties, the solution to this problem, if it exists, is shown to be a unique probability measure, mutually absolutely continuous with the reference measure.

Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis

no code implementations • 9 Feb 2022 • Samir M. Perlaza, Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, Stefano Rini

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure.

On polarised class groups of orders in quartic CM-fields

2 code implementations • 15 Feb 2013 • Gaetan Bisson, Marco Streng

We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group.

Number Theory 11R65, 11G15