Related papers: Discriminating Tail Behavior Using Halfspace Depth…

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

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…

As the data scale grows, deep recognition models often suffer from long-tailed data distributions due to the heavy imbalanced sample number across categories. Indeed, real-world data usually exhibit some similarity relation among different…

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

In this paper, we consider the state-dependent reflecting random walk on a half-strip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed…

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

This paper considers learning deep features from long-tailed data. We observe that in the deep feature space, the head classes and the tail classes present different distribution patterns. The head classes have a relatively large spatial…

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…

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…

A recent line of empirical studies has demonstrated that SGD might exhibit a heavy-tailed behavior in practical settings, and the heaviness of the tails might correlate with the overall performance. In this paper, we investigate the…

This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito…

In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…

A scan statistic is examined for the purpose of testing the existence of a global peak in a random process with dependent variables of any distribution. The scan statistic tail probability is obtained based on the covariance of the moving…

Deploying deep models in real-world scenarios entails a number of challenges, including computational efficiency and real-world (e.g., long-tailed) data distributions. We address the combined challenge of learning long-tailed distributions…

High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…

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…

Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…