Related papers: Multilevel and multifidelity uncertainty quantific…

Effectively measuring and modeling the reliability of a trained model is essential to the real-world deployment of monocular depth estimation (MDE) models. However, the intrinsic ill-posedness and ordinal-sensitive nature of MDE pose major…

Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…

Multifidelity uncertainty propagation combines the efficiency of low-fidelity models with the accuracy of a high-fidelity model to construct statistical estimators of quantities of interest. It is well known that the effectiveness of such…

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

Delivering meaningful uncertainty estimates is essential for a successful deployment of machine learning models in the clinical practice. A central aspect of uncertainty quantification is the ability of a model to return predictions that…

Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution.…

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and…

Control variates are variance reduction techniques for Monte Carlo estimators. They play a critical role in improving Monte Carlo estimators in scientific and machine learning applications that involve computationally expensive integrals.…

Computational models are continuously integrated in the clinical space, where they support clinicians in disease diagnosis, prognosis, and prevention strategies. While assisting in clinical space, these computational models frequently use…

We consider the problem of forecasting debt recovery from large portfolios of non-performing unsecured consumer loans under management. The state of the art in industry is to use stochastic processes to approximately model payment behaviour…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

Improving calibration performance in deep learning (DL) classification models is important when planning the use of DL in a decision-support setting. In such a scenario, a confident wrong prediction could lead to a lack of trust and/or harm…

Uncertainty quantification approaches have been more critical in large language models (LLMs), particularly high-risk applications requiring reliable outputs. However, traditional methods for uncertainty quantification, such as…

In a data-scarce field such as healthcare, where models often deliver predictions on patients with rare conditions, the ability to measure the uncertainty of a model's prediction could potentially lead to improved effectiveness of decision…

We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across…

This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…

Mass cytometry technology enables the simultaneous measurement of over 40 proteins on single cells. This has helped immunologists to increase their understanding of heterogeneity, complexity, and lineage relationships of white blood cells.…

We introduce a novel approach for calibrating uncertainty quantification (UQ) tailored for multi-modal large language models (LLMs). Existing state-of-the-art UQ methods rely on consistency among multiple responses generated by the LLM on…

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…