Related papers: Qualitative Measures of Ambiguity
In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
We study the understanding of deep neural networks from the scope in which they are trained on. While the accuracy of these models is usually impressive on the aggregate level, they still make mistakes, sometimes on cases that appear to be…
In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of…
We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level,…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
Preferences for mixing can reveal ambiguity perception and attitude on a single event. The validity of the approach is discussed for multiple preference classes including maxmin, maxmax, variational, and smooth second-order preferences. An…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Using the known duality between events and states, we establish the fact that there is a duality between quantization of events and measurement of states. With this duality, we will show a generalized system of imprimitivity and a covariant…
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…
There is available an ever-increasing variety of procedures for managing uncertainty. These methods are discussed in the literature of artificial intelligence, as well as in the literature of philosophy of science. Heretofore these methods…
This paper deals with classifying ambiguities for Multimodal Languages. It evolves the classifications and the methods of the literature on ambiguities for Natural Language and Visual Language, empirically defining an original…
Based on existing ideas in the field of imprecise probabilities, we present a new approach for assessing the reliability of the individual predictions of a generative probabilistic classifier. We call this approach robustness…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…