Related papers: Comparing Poisson and Gaussian channels (extended)
In this work we investigate the behavior of the distortion threshold that can be guaranteed in joint source-channel coding, to within a prescribed excess-distortion probability. We show that the gap between this threshold and the optimal…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…
The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…
We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean…
In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the…
We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…
Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as…
We establish Poisson and compound Poisson approximations for stabilizing statistics of $\beta$-mixing point processes and give explicit rates of convergence. Our findings are based on a general estimate of the total variation distance of a…
In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding…
Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler…
We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums of region-stabilizing (determined by the points of the process within some specified regions) score functions and provide a bound on…
Results of numerical procedure of constructing confidence intervals for parameter of the Poisson distribution of signal events in the presence of background events with known value of parameter of Poisson distribution are presented. It is…
We study trajectories of d-dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V can be associated to a field of traps whose centers location is given by a Poisson…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the…
Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random…