Publications related to Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

Amer Chemical Soc2024

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Toyomu Matsuda

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

Matteo Raphael Tacchi

This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...

New York2023

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Daniel Kuhn, Zhi Chen, Wolfram Wiesemann

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...

2022

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2022

Multi-Level Monte Carlo Methods for Uncertainty Quantification and Risk-Averse Optimisation

Sundar Subramaniam Ganesh

This work aims to study the effects of wind uncertainties in civil engineering structural design. Optimising the design of a structure for safety or operability without factoring in these uncertainties can result in a design that is not robust to these per ...

EPFL2022

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

Maryam Kamgarpour, Kai Ren

We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Minimax rate for optimal transport regression between distributions

Victor Panaretos, Laya Ghodrati

Distribution-on-distribution regression considers the problem of formulating and es-timating a regression relationship where both covariate and response are probability distributions. The optimal transport distributional regression model postulates that th ...

ELSEVIER2022

fGOT: Graph Distances Based on Filters and Optimal Transport

Pascal Frossard, Mireille El Gheche, Hermina Petric Maretic, Giovanni Chierchia

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph dis ...

ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE2022

A Wasserstein-based measure of conditional dependence

Negar Kiyavash, Seyed Jalal Etesami, Kun Zhang

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of ability for group ...

2022

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

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Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Multi-Level Monte Carlo Methods for Uncertainty Quantification and Risk-Averse Optimisation

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

Minimax rate for optimal transport regression between distributions

fGOT: Graph Distances Based on Filters and Optimal Transport

A Wasserstein-based measure of conditional dependence

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Multi-Level Monte Carlo Methods for Uncertainty Quantification and Risk-Averse Optimisation

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Minimax rate for optimal transport regression between distributions

fGOT: Graph Distances Based on Filters and Optimal Transport

A Wasserstein-based measure of conditional dependence