Related papers: P-Sensitive Functions and Localizations
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
A general market model with memory is considered in terms of stochastic functional differential equations. We aim at representation formulae for the sensitivity analysis of the dependence of option prices on the memory. This implies a…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…
Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to…
Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability value at a time and observing how this affects output probabilities of interest. When one probability is varied then others are…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
We study robustness to test-time adversarial attacks in the regression setting with $\ell_p$ losses and arbitrary perturbation sets. We address the question of which function classes are PAC learnable in this setting. We show that classes…
Risk and utility functionals are fundamental building blocks in economics and finance. In this paper we investigate under which conditions a risk or utility functional is sensitive to the accumulation of losses in the sense that any…
This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Machine learning models are vulnerable to tiny adversarial input perturbations optimized to cause a very large output error. To measure this vulnerability, we need reliable methods that can find such adversarial perturbations. For image…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…