Related papers: Heavy-Tail Distribution from Correlation of Discre…

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Real-world data often follows a long-tailed distribution, which makes the performance of existing classification algorithms degrade heavily. A key issue is that samples in tail categories fail to depict their intra-class diversity. Humans…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…

In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…

Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel availability dynamics is modeled as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period of time…

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…

Reinforcement learning algorithms typically assume rewards to be sampled from light-tailed distributions, such as Gaussian or bounded. However, a wide variety of real-world systems generate rewards that follow heavy-tailed distributions. We…

Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on…

We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…

The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of…

We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the…

The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…

In a previous work, the authors proposed a Grammatical Evolution algorithm to automatically generate Lindenmayer Systems which represent fractal curves with a pre-determined fractal dimension. This paper gives strong statistical evidence…

The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an…

Networks with stochastic variables described by heavy tailed lognormal distribution are ubiquitous in nature, and hence they deserve an exact information-theoretic characterization. We derive analytical formulas for mutual information…

We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has an heavy-tailed distribution. We also establish that this process is a scaling limit of a process of rumor…

Neurons process sensory stimuli efficiently, showing sparse yet highly variable ensemble spiking activity involving structured higher-order interactions. Notably, while neural populations are mostly silent, they occasionally exhibit highly…