Publications de Amedeo Roberto Esposito

Lower Bounds on the Bayesian Risk via Information Measures

Michael Christoph Gastpar, Adrien Vandenbroucque, Amedeo Roberto Esposito

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually any information measure, including Rényi's α, φ-divergences, and Sibson's α-Mutual Information. The appr ...

2024

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

On Sibson’s α-Mutual Information

Michael Christoph Gastpar, Adrien Vandenbroucque, Amedeo Roberto Esposito

2022

From Generalisation Error to Transportation-cost Inequalities and Back

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we connect the problem of bounding the expected generalisation error with transportation-cost inequalities. Exposing the underlying pattern behind both approaches we are able to generalise them and go beyond Kullback- Leibler Divergences/Mutu ...

2022

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Michael Christoph Gastpar, Adrien Vandenbroucque, Amedeo Roberto Esposito

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of f-Divergences. The results are then applied to specific settings of interest and compared to other notable results i ...

2022

On conditional Sibson's alpha-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we analyse how to define a conditional version of Sibson's alpha-Mutual Information. Several such definitions can be advanced and they all lead to different information measures with different (but similar) operational meanings. We will analy ...

IEEE2021

Lower-bounds on the Bayesian Risk in estimation procedures via Sibson's alpha-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we consider the problem of parameter estimation in a Bayesian setting. We propose a new approach to lower-bounding the Bayesian risk, based on Sibson's alpha-Mutual Information. The results are then applied to specific settings of interest. A ...

IEEE2021

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021

Robust Generalization via f−Mutual Information

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

Given two probability measures P and Q and an event E, we provide bounds on P(E) in terms of Q(E) and f-divergences. In particular, the bounds are instantiated when the measures considered are a joint distribution and the corresponding product of marginals ...

IEEE2020

Robust Generalization via $\alpha$-Mutual Information

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

The aim of this work is to provide bounds connecting two probability measures of the same event using Rényi

\alpha

-Divergences and Sibson’s

\alpha

-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence and Shannon’s Mutual ...

ETHZ2020

Strengthened Information-theoretic Bounds on the Generalization Error

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

The following problem is considered: given a joint distribution P XY and an event E, bound P XY (E) in terms of P X P Y (E) (where P X P Y is the product of the marginals of P XY ) and a measure of dependence of X and Y. Such bounds have direct application ...

IEEE2019

Learning and Adaptive Data Analysis via Maximal Leakage

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

There has been growing interest in studying connections between generalization error of learning algorithms and information measures. In this work, we generalize a result that employs the maximal leakage, a measure of leakage of information, and explore ho ...

IEEE2019