Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification

07/10/2020
by   L. Bonnet, et al.
0

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, we assume that the observational data arise from optimisation problems with partially controllable one-sided errors, and this setting alters several characteristics of the problem and opens natural algorithmic possibilities. Our algorithm uses imperfect evaluations of the target function to direct further evaluations of the target function either at new sites in the function's domain or to improve the quality of evaluations at already-evaluated sites. We establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method both to synthetic test cases and to a real-world example of uncertainty quantification for aerodynamic design.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/17/2020

Uncertainty Quantification in Case of Imperfect Models: A Review

Uncertainty quantification of complex technical systems is often based o...
research
02/08/2018

Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

A variety of methods is available to quantify uncertainties arising with...
research
08/24/2023

Object level footprint uncertainty quantification in infrastructure based sensing

We examine the problem of estimating footprint uncertainty of objects im...
research
08/31/2020

Direct Volume Rendering with Nonparametric Models of Uncertainty

We present a nonparametric statistical framework for the quantification,...
research
09/11/2012

Query Complexity of Derivative-Free Optimization

This paper provides lower bounds on the convergence rate of Derivative F...
research
05/29/2023

Optimal approximation of infinite-dimensional holomorphic functions

Over the last decade, approximating functions in infinite dimensions fro...

Please sign up or login with your details

Forgot password? Click here to reset