Related papers: A Unified framework for order-of-magnitude confide…

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…

A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…

This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…

Over time, there have hen refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distributions depict a complete ordering among the propositions of interest, yet…

Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…

Predictions of uncertainty-aware models are diverse, ranging from single point estimates (often averaged over prediction samples) to predictive distributions, to set-valued or credal-set representations. We propose a novel unified…

In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such…

Uncertainty in machine learning refers to the degree of confidence or lack thereof in a model's predictions. While uncertainty quantification methods exist, explanations of uncertainty, especially in high-dimensional settings, remain an…

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…

The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand a candidate can be evaluated according to different criteria, and on the other hand several experts are supposed to assess…

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…

Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following…

Considering the high heterogeneity of the ontologies pub-lished on the web, ontology matching is a crucial issue whose aim is to establish links between an entity of a source ontology and one or several entities from a target ontology.…

Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the…

Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we…

We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…

We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…