Related papers: A Theory of Uncertainty Variables for State Estima…

Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…

Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…

In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…

We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…

Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…

Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model…

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…

Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear…

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…