Related papers: Asymptotic Classification Error for Heavy-Tailed R…

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index…

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…

We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…

In this entry we review the generalization error for classification and single-stage decision problems. We distinguish three alternative definitions of the generalization error which have, at times, been conflated in the statistics…

We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the…

In this paper, we develop sample path large deviations for multivariate Hawkes processes with heavy-tailed mutual excitation rates. Our results address a broad class of rare events in Hawkes processes at the sample path level and, via the…

Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…

In this paper, we establish the asymptotic behavior of {\it supercritical} nearly unstable Hawkes processes with a power law kernel. We find that, the Hawkes process in our context admits a similar equation to that in \cite{MR3563196} for…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest…

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the…

In this paper we determine bounds and exact asymptotics of the ruin probability for risk process with arrivals given by a linear marked Hawkes process. We consider the light-tailed and heavy-tailed case of the claim sizes. Main technique is…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result,…

Recently, long-tailed image classification harvests lots of research attention, since the data distribution is long-tailed in many real-world situations. Piles of algorithms are devised to address the data imbalance problem by biasing the…

We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…

In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…

We study the asymptotic behaviour of the survival probability of a multitype branching process in random environment. The class of processes we consider here corresponds, in the one-dimensional situation, to the strongly subcritical case.…

We present an algorithm for distributed estimation of an unknown vector parameter $\boldsymbol{\theta}^\ast \in {\mathbb R}^M$ in the presence of heavy-tailed observation and communication noises. Heavy-tailed noises frequently appear,…