Related papers: Unifying Practical Uncertainty Representations: I.…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…
We develop a general theory for estimating the probability that a galaxy cluster of a given shape exists. The theory is based on the observed result that the distribution of galaxies is very close to quasi-equilibrium, in both its linear…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…
The generalized parton distributions are non-perturbative objects, which encode information on long distance dynamics in a number of exclusive processes. They are hybrids of conventional parton densities, distribution amplitudes and hadron…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
Multiplicative invariance is a well-studied property of subsets of the unit interval. The theory in the complex plane is less developed. This paper introduces an analogous definition for multiplicative invariance in the complex plane…