Related papers: Rounding Effects in Record Statistics
Having reliable estimates of the occurrence rates of extreme events is highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period,…
We study the effectiveness of randomizing split-directions in random forests. Prior literature has shown that, on the one hand, randomization can reduce variance through decorrelation, and, on the other hand, randomization regularizes and…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al.…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
This article is about discrete periodicities and their combinatorial structure. It describes the unique structure caused by the alteration of a pattern in a repetition. That alteration of a pattern could be "heard" as the disturbance that…
Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete…
In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the…
The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification of randomness based…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
Records among a sequence of iid random variables $X_1,X_2,\dotsc$ on the real line have been investigated extensively over the past decades. A record is defined as a random variable $X_n$ such that $X_n>\max(X_1,\dotsc,X_{n-1})$. Trying to…
Recently there has been much work on selective sampling, an online active learning setting, in which algorithms work in rounds. On each round an algorithm receives an input and makes a prediction. Then, it can decide whether to query a…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite…
We develop a Difference-in-Differences framework for discrete, ordered outcomes subject to underreporting. Such outcomes commonly arise in self-reported surveys on socially undesirable or stigmatized behaviors, where respondents may conceal…
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 paper focuses on nonparametric statistical inference of the hazard rate function of discrete distributions based on $\delta$-record data. We derive the explicit expression of the maximum likelihood estimator and determine its exact…
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…