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One of the most profound challenges of modern machine learning is performing well on the long-tail of rare and underrepresented features. Large general-purpose models are trained for many tasks, but work best on high-frequency use cases.…
The main contribution of this paper is to prove the subexponential tail equivalence of the stationary queue length distributions in the BMAP/GI/1 queues with and without retrials. We first present a stochastic-decomposition-like result of…
In this article a special case of an M/G/2-queue is considered, where the two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model the asymptotic behaviour of the workload buffer…
In this paper we first provide several conditional limit theorems for L\'evy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of…
Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…
We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ and a sequence of i.i.d. $X$-valued random variables $\xi_1,\dots,\xi_n$, and give a good estimate on the tail behaviour of $\sup\limits_{f\in\Cal…
In this paper, we consider how to provide fast estimates of flow-level tail latency performance for very large scale data center networks. Network tail latency is often a crucial metric for cloud application performance that can be affected…
We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…
For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from…
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic…
We consider the problem of packet scheduling in single-hop queueing networks, and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric we use the delay stability of traffic flows: a…
Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on…
This paper investigates the phenomenon of benign overfitting in binary classification problems with heavy-tailed input distributions, extending the analysis of maximum margin classifiers to $\alpha$ sub-exponential distributions ($\alpha…
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized…
Deploying Python-based AI agents on resource-constrained edge devices presents a critical runtime optimization challenge: high thread counts are needed to mask I/O latency, yet Python's Global Interpreter Lock (GIL) serializes execution. We…
We consider a problem on the synthesis of reactive controllers that optimize some a priori unknown performance criterion while interacting with an uncontrolled environment such that the system satisfies a given temporal logic specification.…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
We consider the tail behavior of random variables $R$ which are solutions of the distributional equation $R\stackrel{d}{=}Q+MR$, where $(Q,M)$ is independent of $R$ and $|M|\le 1$. Goldie and Gr\"{u}bel showed that the tails of $R$ are no…