相关论文: Records in a changing world
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
This paper proposes a scoring-rule-based method for ranking predictive distributions in the Fr\'echet domain that is able to distinguish between different tail indices. The approach is built on normalized order statistics and exploits…
We develop formal privacy mechanisms for releasing statistics from data with many outlying values, such as income data. These mechanisms ensure that a per-record differential privacy guarantee degrades slowly in the protected records'…
The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
In this paper we characterize the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. The extremal sums behave completely different by compared to…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
Correlations in music that exist within its waveform are studied. Monophonic wave files of random music are generated and the probability distribution function of time interval between large signal values is analyzed. A power law behavior…
Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These…
Doron Gepner's word statistics, that came up in his research in conformal field theory, is studied and it is conjectured that its scaled limiting distribution is the Logistic distribution. We support this by proving rigorously that the…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
Taylor's law (TL) states that the variance $V$ of a non-negative random variable is a power function of its mean $M$, i.e. $V=a M^b$. The ubiquitous empirical verification of TL, typically displaying sample exponents $b \simeq 2$, suggests…
Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution \emph{rank diversity}. We calculate this diversity…
It is well known that a Lorenz curve, derived from the distribution function of a random variable, can itself be viewed as a probability distribution function of a new random variable [4]. In a previous work of ours [26], we proved the…
This study investigates the emergence of power-law and other concentrated distributions through a feedback loop model in crowd interactions. Agents act by their response functions to observations and external forces, while observations…
Compositional data arise when count observations are normalised into proportions adding up to unity. To allow use of standard statistical methods, compositional proportions can be mapped from the simplex into the Euclidean space through the…
In this paper, we investigate the number of real zeros of random Weyl polynomials of degree \(n \to \infty\) with general coefficient distributions. Motivated by the results of arXiv:1409.4128 and arXiv:1402.4628 as well as arXiv:1711.03316…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
Variational inference is a powerful tool for approximate inference. However, it mainly focuses on the evidence lower bound as variational objective and the development of other measures for variational inference is a promising area of…