Related papers: Partially Specified Belief Functions
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…
Although pretrained language models (PTLMs) contain significant amounts of world knowledge, they can still produce inconsistent answers to questions when probed, even after specialized training. As a result, it can be hard to identify what…
One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent,…
One of the core assumptions in causal discovery is the faithfulness assumption, i.e., assuming that independencies found in the data are due to separations in the true causal graph. This assumption can, however, be violated in many ways,…
This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal…
A principle is modified that underlies the theory of organic fiducial inference as this theory was presented in an earlier paper. This modification, which is arguably a natural one to make, allows Bayesian inference to sometimes have a…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially…
A feature-based model explanation denotes how much each input feature contributes to a model's output for a given data point. As the number of proposed explanation functions grows, we lack quantitative evaluation criteria to help…
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…
This Point spread function (PSF) plays a crucial role in many computational imaging applications, such as shape from focus/defocus, depth estimation, and fluorescence microscopy. However, the mathematical model of the defocus process is…
A common approach to explaining NLP models is to use importance measures that express which tokens are important for a prediction. Unfortunately, such explanations are often wrong despite being persuasive. Therefore, it is essential to…
The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…
We present a new algorithm for finding maximum a-posterior) (MAP) assignments of values to belief networks. The belief network is compiled into a network consisting only of nodes with boolean (i.e. only 0 or 1) conditional probabilities.…
In the theory of Partially Observed Markov Decision Processes (POMDPs), existence of optimal policies have in general been established via converting the original partially observed stochastic control problem to a fully observed one on the…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
We study minimal single-task peer prediction mechanisms that have limited knowledge about agents' beliefs. Without knowing what agents' beliefs are or eliciting additional information, it is not possible to design a truthful mechanism in a…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Belief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the…
Whereas deterministic protocols are typically guaranteed to obtain particular goals of interest, probabilistic protocols typically provide only probabilistic guarantees. This paper initiates an investigation of the interdependence between…