Related papers: Unified Framework for Hybrid Aleatory and Epistemi…

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…

Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter…

Most existing federated learning methods are unable to estimate model/predictive uncertainty since the client models are trained using the standard loss function minimization approach which ignores such uncertainties. In many situations,…

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…

Decomposing predictive uncertainty into epistemic (model ignorance) and aleatoric (data ambiguity) components is central to reliable decision making, yet most methods estimate both from the same predictive distribution. Recent empirical and…

Accurate overland runoff and infiltration predictions are critical for effective water resources management, in particular for urban flood management. However, the inherent uncertainty in rainfall patterns, soil properties, and initial…

We introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white…

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…

Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with…

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…

This paper presents a hierarchical decision-making framework for autonomous systems operating under uncertainty, demonstrated through autonomous driving as a representative application. Surrounding agents are modeled using Hybrid Markov…

We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynamical systems generated by uncertain (Eulerian) vector…

Supervised masking approaches in the time-frequency domain aim to employ deep neural networks to estimate a multiplicative mask to extract clean speech. This leads to a single estimate for each input without any guarantees or measures of…

We present Epistemic Variational Onsager Diffusion Models (EVODMs), a machine learning framework that integrates Onsager's variational principle with diffusion models to enable thermodynamically consistent learning of free energy and…

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A mathematically exact…

Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal…

This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard…

In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and…