Publications related to Approaches to Conditional Risk

The ABCD of topological recursion

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...

San Diego2024

Persistence and the Sheaf-Function Correspondence

Nicolas Michel Berkouk

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold M with the Grothendieck group of constructible sheaves on M. When M is a finite dimensional real vector space, Kashiwara-Schapira have recently in ...

Cambridge2023

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

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

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

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

Fabio Nobile, Sebastian Krumscheid, Sundar Subramaniam Ganesh

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...

2022

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

Stochastic distributed learning with gradient quantization and double-variance reduction

Sebastian Urban Stich, Konstantin Mishchenko

We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...

TAYLOR & FRANCIS LTD2022

Mean-Covariance Robust Risk Measurement

Daniel Kuhn, Damir Filipovic, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population dis ...

2021

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Approaches to Conditional Risk

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The ABCD of topological recursion

Persistence and the Sheaf-Function Correspondence

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

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

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

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

A Functional Perspective on Information Measures

Stochastic distributed learning with gradient quantization and double-variance reduction

Mean-Covariance Robust Risk Measurement

A first-order primal-dual method with adaptivity to local smoothness

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

Persistence and the Sheaf-Function Correspondence

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

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

A Functional Perspective on Information Measures

The ABCD of topological recursion

A first-order primal-dual method with adaptivity to local smoothness

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

Mean-Covariance Robust Risk Measurement

Stochastic distributed learning with gradient quantization and double-variance reduction