Related papers: Inclusion within Continuous Belief Functions

The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only…

There is broad agreement in the literature that explanation methods should be faithful to the model that they explain, but faithfulness remains a rather vague term. We revisit faithfulness in the context of continuous data and propose two…

In the existing evidential networks with belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions…

The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into…

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and…

Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…

In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using…

As large language models (LLMs) continue to demonstrate remarkable abilities across various domains, computer scientists are developing methods to understand their cognitive processes, particularly concerning how (and if) LLMs internally…

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…

Large language models have the potential to generate explanations for their own predictions in a variety of styles based on user instructions. Recent research has examined whether these self-explanations faithfully reflect the models'…

We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…

We motivate and describe a theory of belief in this paper. This theory is developed with the following view of human belief in mind. Consider the belief that an event E will occur (or has occurred or is occurring). An agent either…

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…

An overview is presented of a general theory of statistical inference that is referred to as the fiducial-Bayes fusion. This theory combines organic fiducial inference and Bayesian inference. The aim is that the reader is given a clear…

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…

A myriad of explainability methods have been proposed in recent years, but there is little consensus on how to evaluate them. While automatic metrics allow for quick benchmarking, it isn't clear how such metrics reflect human interaction…

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…

In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…

This paper will focus on the process of 'fusing' several observations or models of uncertainty into a single resultant model. Many existing approaches to fusion use subjective quantities such as 'strengths of belief' and process these…

Do norms of rationality apply to machine learning models, in particular language models? In this paper we investigate this question by focusing on a special subset of rational norms: coherence norms. We consider both logical coherence norms…