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Uncertainty quantification is a key pillar of trustworthy machine learning. It enables safe reactions under unsafe inputs, like predicting only when the machine learning model detects sufficient evidence, discarding anomalous data, or…

Many practical scenarios make it necessary to evaluate top-k queries over data items with partially unknown values. This paper considers a setting where the values are taken from a numerical domain, and where some partial order constraints…

Dempster-Shafer theory is widely applied to uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. However, some conditions, such as exclusiveness hypothesis and completeness constraint, limit…

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…

In the probabilistic approach to uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability…

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…

Propositional representation services such as truth maintenance systems offer powerful support for incremental, interleaved, problem-model construction and evaluation. Probabilistic inference systems, in contrast, have lagged behind in…

The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…

The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…

Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…

Learning is a distinctive feature of intelligent behaviour. High-throughput experimental data and Big Data promise to open new windows on complex systems such as cells, the brain or our societies. Yet, the puzzling success of Artificial…

We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…

This paper describes the incorporation of uncertainty in diagnostic reasoning based on the set covering model of Reggia et. al. extended to what in the Artificial Intelligence dichotomy between deep and compiled (shallow, surface) knowledge…

An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…

An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…

The study of the brain's representations of uncertainty is a central topic in neuroscience. Unlike most quantities of which the neural representation is studied, uncertainty is a property of an observer's beliefs about the world, which…

Predictive uncertainty estimation of pre-trained language models is an important measure of how likely people can trust their predictions. However, little is known about what makes a model prediction uncertain. Explaining predictive…

This paper addresses a significant gap in explainable AI: the necessity of interpreting epistemic uncertainty in model explanations. Although current methods mainly focus on explaining predictions, with some including uncertainty, they fail…