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There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…

Understanding and quantifying uncertainty in black box Neural Networks (NNs) is critical when deployed in real-world settings such as healthcare. Recent works using Bayesian and non-Bayesian methods have shown how a unified predictive…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Testing of deep learning models is challenging due to the excessive number and complexity of computations involved. As a result, test data selection is performed manually and in an ad hoc way. This raises the question of how we can…

The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in…

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…

Clustering uncertain data has emerged as a challenging task in uncertain data management and mining. Thanks to a computational complexity advantage over other clustering paradigms, partitional clustering has been particularly studied and a…

Mathematical models allow us to gain a deeper understanding of real-world dynamical systems. One of the most powerful mathematical frameworks for modeling real-world phenomena are systems of differential equations. In the majority of fields…

Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of…

Categorical random variables can faithfully represent the discrete and uncertain aspects of data as part of a discrete latent variable model. Learning in such models necessitates taking gradients with respect to the parameters of the…

The paper advocates the use of a statistical tool dedicated to the exploration of data samples populated by several sources of events. This new technique, called sPlot, is able to unfold the contributions of the different sources to the…

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…

In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

We present batching as an omnibus device for uncertainty quantification using simulation output. We consider the classical context of a simulationist performing uncertainty quantification on an estimator $\theta_n$ (of an unknown fixed…

We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…

Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…

In this paper, we leverage predictive uncertainty of deep neural networks to answer challenging questions material scientists usually encounter in machine learning based materials applications workflows. First, we show that by leveraging…

We present Korali, an open-source framework for large-scale Bayesian uncertainty quantification and stochastic optimization. The framework relies on non-intrusive sampling of complex multiphysics models and enables their exploitation for…