Related papers: Refined Stratified Sampling for efficient Monte Ca…

The curse of dimensionality presents a pervasive challenge in optimization problems, with exponential expansion of the search space rapidly causing traditional algorithms to become inefficient or infeasible. An adaptive sampling strategy is…

In this paper we suggest a modification of the regression-based variance reduction approach recently proposed in Belomestny et al. This modification is based on the stratification technique and allows for a further significant variance…

Randomized smoothing (RS) has been shown to be a fast, scalable technique for certifying the robustness of deep neural network classifiers. However, methods based on RS require augmenting data with large amounts of noise, which leads to…

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

It is critical and challenging to design robust predictors for stochastic dynamical systems (SDSs) with uncertainty quantification (UQ) in the prediction. Specifically, robustness guarantees the worst-case performance when the predictor's…

Domain shift remains a key challenge in deploying machine learning models to the real world. Unsupervised domain adaptation (UDA) aims to address this by minimising domain discrepancy during training, but the discrepancy estimates suffer…

Optimizing the reliability and the robustness of a design is important but often unaffordable due to high sample requirements. Surrogate models based on statistical and machine learning methods are used to increase the sample efficiency.…

Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…

Uncertainties from model parameters and model discrepancy from small-scale models impact the accuracy and reliability of predictions of large-scale systems. Inadequate representation of these uncertainties may result in inaccurate and…

The introduction of the Segment Anything Model (SAM) has paved the way for numerous semantic segmentation applications. For several tasks, quantifying the uncertainty of SAM is of particular interest. However, the ambiguous nature of the…

The Robust Satisficing (RS) model is an emerging approach to robust optimization, offering streamlined procedures and robust generalization across various applications. However, the statistical theory of RS remains unexplored in the…

The performance of a machine learning system is usually evaluated by using i.i.d.\ observations with true labels. However, acquiring ground truth labels is expensive, while obtaining unlabeled samples may be cheaper. Stratified sampling can…

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…

Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines,…

Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an…

Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its…

Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…

In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…

Uncertainty quantification (UQ) in deep learning regression is of wide interest, as it supports critical applications including sequential decision making and risk-sensitive tasks. In heteroskedastic regression, where the uncertainty of the…