Related papers: Tail Index Estimation for Discrete Heavy-Tailed Di…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…
Unraveling the reasons behind the remarkable success and exceptional generalization capabilities of deep neural networks presents a formidable challenge. Recent insights from random matrix theory, specifically those concerning the spectral…
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…
Given $n$ samples from a population of individuals belonging to different species, what is the number $U$ of hitherto unseen species that would be observed if $\lambda n$ new samples were collected? This is an important problem in many…
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…
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 consider the probability that a weighted sum of $n$ i.i.d. random variables $X_j$, $j = 1, . . ., n$, with stretched exponential tails is larger than its expectation and determine the rate of its decay, under suitable conditions on the…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically…
The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm. While many works provide high-probability guarantees, quantifying…
In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale under norming sequence 1/n, as in the classical Law of Large Numbers (LLN), by means of martingale differences…
In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and…
How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…
Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as…
We study the lower tail large deviation problem for subgraph counts in a random graph. Let $X_H$ denote the number of copies of $H$ in an Erd\H{o}s-R\'enyi random graph $\mathcal{G}(n,p)$. We are interested in estimating the lower tail…
Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are…
Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…