Related papers: Strong Asymptotic Composition Theorems for Mutual …
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
We review recent progress in understanding the meaning of mutual information in natural language. Let us define words in a text as strings that occur sufficiently often. In a few previous papers, we have shown that a power-law distribution…
Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual…
We consider time-inhomogeneous ODEs whose parameters are governed by an underlying ergodic Markov process. When this underlying process is accelerated by a factor $\varepsilon^{-1}$, an averaging phenomenon occurs and the solution of the…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…
Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
Sensor placement approaches in networks often involve using information-theoretic measures such as entropy and mutual information. We prove that mutual information abides by submodularity and is non-decreasing when considering the mutual…
First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a…
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…
Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…
This study confirms a local trade-off between information and disturbance in quantum measurements. It is represented by the correlation between the changes in these two quantities when the measurement is slightly modified. The correlation…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
The dynamical emergence (and subsequent intermittent breakdown) of collective behavior in complex systems is described as a non-Poisson renewal process, characterized by a waiting-time distribution density $\psi (\tau)$ for the time…
We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are…
The existing consensus is that flocks are poised at criticality, entailing long correlation lengths and a maximal value of Shannon mutual information in the large-system limit. We show, by contrast, that for finite flocks in the long…