Publications related to Probability space

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

COVID-19: data-driven dynamic asset allocation in times of pandemic

Anna Timonina-Farkas

The COVID-19 pandemic has demonstrated the importance and value of multi-period asset allocation strategies responding to rapid changes in market behavior. In this article, we formulate and solve a multi-stage stochastic optimization problem, choosing the ...

AMER INST MATHEMATICAL SCIENCES-AIMS2021

A General Framework for Optimal Data-Driven Optimization

Daniel Kuhn, Tobias Sutter

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...

2021

Wasserstein Adversarial Regularization for learning with label noise

Devis Tuia, Sylvain Lobry, Nicolas Courty

Noisy labels often occur in vision datasets, especially when they are obtained from crowdsourcing or Web scraping. We propose a new regularization method, which enables learning robust classifiers in presence of noisy data. To achieve this goal, we propose ...

2021

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

Daniel Maria Busiello, Deepak Gupta

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the th ...

2020

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

Normalized Gaussian path integrals

Giulio Corazza

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...

AMER PHYSICAL SOC2020

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Volkan Cevher, Ali Kavis, Shaul Nadav Hallak

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

2020

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fabio Nobile, Francesca Bonizzoni, Davide Pradovera

The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...

2020

The Cost of Scaling a Reliable Interconnection Topology

Rachid Guerraoui, Alexandre David Olivier Maurer

In distributed computing, many papers try to evaluate the message complexity of a distributed system as a function of the number of nodes n. But what about the cost of building the distributed system itself? Assuming that we want to reliably connect n node ...

2020

Probability space

Graph Chatbot

Chat with Graph Search

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

COVID-19: data-driven dynamic asset allocation in times of pandemic

A General Framework for Optimal Data-Driven Optimization

Wasserstein Adversarial Regularization for learning with label noise

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

Robust Generalization via $\alpha$-Mutual Information

Normalized Gaussian path integrals

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

The Cost of Scaling a Reliable Interconnection Topology

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

COVID-19: data-driven dynamic asset allocation in times of pandemic

A General Framework for Optimal Data-Driven Optimization

The Cost of Scaling a Reliable Interconnection Topology

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Wasserstein Adversarial Regularization for learning with label noise

Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions

Robust Generalization via $\alpha$-Mutual Information

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Normalized Gaussian path integrals