Related papers: A gradient-enhanced univariate dimension reduction…

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated…

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…

Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…

We present Re-weighted Gradient Descent (RGD), a novel optimization technique that improves the performance of deep neural networks through dynamic sample re-weighting. Leveraging insights from distributionally robust optimization (DRO)…

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…

Modern representation learning methods often struggle to adapt quickly under non-stationarity because they suffer from catastrophic forgetting and decaying plasticity. Such problems prevent learners from fast adaptation since they may…

Uncertainty quantification is critical for deploying deep neural networks (DNNs) in real-world applications. An Auxiliary Uncertainty Estimator (AuxUE) is one of the most effective means to estimate the uncertainty of the main task…

Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the…

Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…

We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…

Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…

The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves)…

Stochastic Gradient Descent (SGD) is a widely used tool in machine learning. In the context of Differential Privacy (DP), SGD has been well studied in the last years in which the focus is mainly on convergence rates and privacy guarantees.…

Development of an accurate, flexible, and numerically efficient uncertainty quantification (UQ) method is one of fundamental challenges in machine learning. Previously, a UQ method called DISCO Nets has been proposed (Bouchacourt et al.,…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…

Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them,…

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…

Uncertainty quantification (UQ) for foundation models is essential to identify and mitigate potential hallucinations in automatically generated text. However, heuristic UQ approaches lack formal guarantees for key metrics such as the false…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…