Uncertainty Quantification by Random Measures and Fields

Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this work, we combine such variational formulas with functional inequalities (Poincar{é}, $\log$-Sobolev, Liapunov functions) to derive explicit uncertainty quantification bounds for time-averaged observables, comparing a Markov process to a second (not necessarily Markov) process. These bounds are well-behaved in the infinite-time limit and apply to steady-states of…

Scalable Information Inequalities for Uncertainty Quantification

In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for quantities of interest in the large degree of freedom limit and/or at long time regimes; (b) assess the impact of large model perturbations as in nonlinear response regimes in statistical mechanics; (c) address model-form uncertainty, i.e. compare different extended models and corresponding quantities of interest. We demonstrate some of these properties by derivi…

Formulation and properties of a divergence used to compare probability measures without absolute continuity and its application to uncertainty quantification

This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. We include examples of computation and approximation of the divergence, and its applications in uncertainty quantification in discrete models and Gauss-Markov models.

Uncertainty quantification with risk measures in production planning

This paper is concerned with a simulation study for a stochastic production network model, where the capacities of machines may change randomly. We introduce performance measures motivated by risk measures from finance leading to a simulation based optimization framework for the production planning. The same measures are used to investigate the scenario when capacities are related to workers that are randomly not available. This corresponds to the study of a workforce planning problem in an uncertain environment.

Transformer模型在暗模式检测中的不确定性量化

Uncertainty Quantification for Transformer Models for Dark-Pattern Detection

针对Transformer模型在暗模式检测中的不透明性问题，提出差异微调结合SNGPs/BNNs不确定性量化方法，在保持性能的同时提升透明度与可解释性，为高可信度模型开发提供支持。