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Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional…
We propose a model for diffusion of two opposite opinions. Here, the decision to be taken by each individual is a random variable which depends on the tendency of the population, as well on its own trend characteristic. The influence of the…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…
When machine-learning algorithms are used in high-stakes decisions, we want to ensure that their deployment leads to fair and equitable outcomes. This concern has motivated a fast-growing literature that focuses on diagnosing and addressing…
A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist)…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
Modern Artificial Intelligence achieves remarkable predictive power by optimizing statistical risk functionals over vast corpora. Yet a gap separates this from genuine intelligence: the inability to distinguish correlation from causation.…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
We build simple computational models of belief dynamics within the framework of discrete-spin statistical physics models, and explore how suitable they are for understanding and predicting real-world belief change on both the individual and…
Displaying confidence scores in human-AI interaction has been shown to help build trust between humans and AI systems. However, most existing research uses only the confidence score as a form of communication. As confidence scores are just…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
Datasets for training recommender systems are often subject to distribution shift induced by users' and recommenders' selection biases. In this paper, we study the impact of selection bias on datasets with different quantization. We then…
In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…
There are two distinct definitions of 'P-value' for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was…