Related papers: Quantization for a mixture of uniform distribution…

This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to…

For uniform scalar quantization, the error distribution is approximately a uniform distribution over an interval (which is also a 1-dimensional ball). Nevertheless, for lattice vector quantization, the error distribution is uniform not over…

This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…

We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…

The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…

Unlike classification, whose goal is to estimate the class of each data point in a dataset, prevalence estimation or quantification is a task that aims to estimate the distribution of classes in a dataset. The two main tasks in prevalence…

Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…

In this paper, we have considered a uniform probability distribution supported by a stretched Sierpi\'nski triangle. For this probability measure, the optimal sets of $n$-means and the $n$th quantization errors are determined for all $n\geq…

Although quality indicators play a crucial role in benchmarking evolutionary multi-objective optimization algorithms, their properties are still unclear. One promising approach for understanding quality indicators is the use of the optimal…

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…

In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular $m$-sided polygons inscribed in a circle. The result shows that the quantization…

In the recent years, the notion of mixability has been developed with applications to optimal transportation, quantitative finance and operations research. An $n$-tuple of distributions is said to be jointly mixable if there exist $n$…

Majorization theory is a powerful mathematical tool to compare the disorder in distributions, with wide-ranging applications in many fields including mathematics, physics, information theory, and economics. While majorization theory…

We consider the problem of distributed feature quantization, where the goal is to enable a pretrained classifier at a central node to carry out its classification on features that are gathered from distributed nodes through communication…

Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…