Related papers: A geometric approach to conditioning belief functi…
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
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,…
This paper presents some ideas to reduce the computational cost of evidence-based robust design optimization. Evidence Theory crystallizes both the aleatory and epistemic uncertainties in the design parameters, providing two quantitative…
A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…
This paper provides an analysis of different formal representations of beliefs in epistemic game theory. The aim is to attempt a synthesis of different structures of beliefs in the presence of indeterminate probabilities. Special attention…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
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…
In a recent paper, Belle and Levesque proposed a framework for a type of program called belief programs, a probabilistic extension of GOLOG programs where every action and sensing result could be noisy and every test condition refers to the…
Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…
Belief revision is an operation that aims at modifying old be-liefs 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…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…