Related papers: Optimization Under Uncertainty Using the Generaliz…
Chance constrained programming (CCP) is a powerful framework for addressing optimization problems under uncertainty. In this paper, we introduce a novel Gradient-Guided Diffusion-based Optimization framework, termed GGDOpt, which tackles…
Geothermal field modeling is often associated with uncertainties related to the subsurface static properties and the dynamics of fluid flow and heat transfer. Uncertainty quantification using simulations is a useful tool to design optimum…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…
A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
Modern computers enable methods for design optimization that account for uncertainty in the system---so-called optimization under uncertainty. We propose a metric for OUU that measures the distance between a designer-specified probability…
We gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. We evaluate the maximum quantile over a class of distributions defined only by constraints…
Quantile Factor Models (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only location-shifting factors can be extracted, QFM also allow to recover unobserved factors…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
Estimates of finite population cumulativedistribution functions (CDFs) and quantiles are critical forpolicy-making, resource allocation, and public health planning. For instance, federal finance agencies may require accurate estimates of…
In inverse problems, distribution-free uncertainty quantification (UQ) aims to obtain error bars with coverage guarantees that are independent of any prior assumptions about the data distribution. In the context of mass mapping,…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
Radiotherapy planning naturally leads to a multi-criteria optimization problem which is subject to different sources of uncertainty. In order to find the desired treatment plan, a decision maker must balance these objectives as well as the…
We present a data-driven Bayesian nonparametric approach for global optimization (DaBNO) of stochastic black-box function. The function value depends on the distribution of a random vector. However, this distribution is usually complex and…
Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by analyzing the generalization error based on the optimization…