Related papers: Contextuality Analysis of Impossible Figures
Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfil the minimal condition of…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…
As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context…
Ontological models are attempts to quantitatively describe the results of a probabilistic theory, such as Quantum Mechanics, in a framework exhibiting an explicit realism-based underpinning. Unlike either the well known quasi-probability…
The sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…
This paper develops an interpretive framework for divergence P-values and S-values within a descriptive frequentist perspective. Statistical analysis is framed as operating within idealized worlds defined by a set of assumptions and a…
The rapid advancement and widespread adoption of machine learning-driven technologies have underscored the practical and ethical need for creating interpretable artificial intelligence systems. Feature importance, a method that assigns…
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…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity'…
This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be described either by a model with free choice but…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from…
Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…