Publications related to Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

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

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

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Wolfram Wiesemann

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood ...

2019

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...

MATHICSE2018

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...

Springer Heidelberg2016

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

MATHICSE2015

Exact soliton-like probability measures for interacting jump processes

Max-Olivier Hongler

The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field (MF) approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The nonlinearity compens ...

2015

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

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

Robust Generalization via $\alpha$-Mutual Information

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Exact soliton-like probability measures for interacting jump processes

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

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

Robust Generalization via $\alpha$-Mutual Information

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Exact soliton-like probability measures for interacting jump processes