Related papers: A geometric approach to conditioning belief functi…
While bibliometrics are widely used for research evaluation purposes, a common theoretical framework for conceptually understanding, empirically studying, and effectively teaching its usage is lacking. In this paper, we outline such a…
The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their…
This paper presents discussions on the limitations of the witness configuration method. These limitations have rarely been reported in previous studies. The witness configuration method is a very recent approach for geometric constraint…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed.…
We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
One aspect of the algorithmic lens in theoretical computer science is a view on other scientific disciplines that focuses on satisfactory solutions that adhere to real-world constraints, as opposed to solutions that would be optimal…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings,…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding…
Mathematical Theory of Evidence (MTE), a foundation for reasoning under partial ignorance, is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
The problem of belief tracking in the presence of stochastic actions and observations is pervasive and yet computationally intractable. In this work we show however that probabilistic beliefs can be maintained in factored form exactly and…