Publications related to Bregman divergence

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

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

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

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

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

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Michael Christoph Gastpar, Adriano Pastore

We consider a setup in which confidential i.i.d. samples X1, . . . , Xn from an unknown finite-support distribution p are passed through n copies of a discrete privatization chan- nel (a.k.a. mechanism) producing outputs Y1, . . . , Yn. The channel law gua ...

2021

Many-body localization in a fragmented Hilbert space

Loïc Jean Pierre Herviou

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...

2021

Robust Generalization via $\alpha$-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

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

Robust Generalization via f−Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

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

Fast Mean Estimation with Sub-Gaussian Rates

Nicolas Henri Bernard Flammarion

We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we make an additional ...

2019

A sequence-dependent coarse-grain model of B-DNA with explicit description of bases and phosphate groups parametrised from large scale Molecular Dynamics simulations

Alessandro Samuele Patelli

We introduce a sequence-dependent coarse-grain model of double-stranded DNA with an explicit description of both the bases and the phosphate groups as interacting rigid-bodies. The model parameters are trained on extensive, state-of-the-art large scale mol ...

EPFL2019

Entropy as a tool for crystal discovery

Pablo Miguel Piaggi

The computational prediction of crystal structures has emerged as an useful alternative to expensive and often cumbersome experiments. We propose an approach to the prediction of crystal structures and polymorphism based on reproducing the crystallization ...

EPFL2019

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From Generalisation Error to Transportation-cost Inequalities and Back

On the commutativity of flows of rough vector fields

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

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Many-body localization in a fragmented Hilbert space

Robust Generalization via $\alpha$-Mutual Information

Robust Generalization via f−Mutual Information

Fast Mean Estimation with Sub-Gaussian Rates

A sequence-dependent coarse-grain model of B-DNA with explicit description of bases and phosphate groups parametrised from large scale Molecular Dynamics simulations

Entropy as a tool for crystal discovery

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

Many-body localization in a fragmented Hilbert space

Robust Generalization via $\alpha$-Mutual Information

Robust Generalization via f−Mutual Information

A sequence-dependent coarse-grain model of B-DNA with explicit description of bases and phosphate groups parametrised from large scale Molecular Dynamics simulations

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Entropy as a tool for crystal discovery

Fast Mean Estimation with Sub-Gaussian Rates

From Generalisation Error to Transportation-cost Inequalities and Back

On the commutativity of flows of rough vector fields