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Anomaly detection has many applications ranging from bank-fraud detection and cyber-threat detection to equipment maintenance and health monitoring. However, choosing a suitable algorithm for a given application remains a challenging design…

In response to the demand for higher computational power, the number of computing nodes in high performance computers (HPC) increases rapidly. Exascale HPC systems are expected to arrive by 2020. With drastic increase in the number of HPC…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-21 Siavash Ghiasvand , Florina M. Ciorba

We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…

Quantum Physics · Physics 2024-03-27 Giulio Gasbarri , Matias Bilkis , Elisabet Roda-Salichs , John Calsamiglia

In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…

Statistics Theory · Mathematics 2018-11-26 Holger Dette , Josua Gösmann

Detecting anomalies in time series data is a challenging task with broad relevance in many applications. Existing methods work effectively only under idealized conditions, typically focusing on point anomalies or assuming a constant…

Methodology · Statistics 2025-09-01 Yiyin Zhang , Florian Pein , Idris Eckley

This paper presents a new approach, based on polynomial optimization and the method of moments, to the problem of anomaly detection. The proposed technique only requires information about the statistical moments of the normal-state…

Optimization and Control · Mathematics 2015-06-02 Jose A. Lopez , Octavia Camps , Mario Sznaier

Sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence. In this problem, the common probability law of a sequence of i.i.d. random…

Probability · Mathematics 2007-10-29 Savas Dayanik , Christian Goulding , H. Vincent Poor

Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information…

Artificial Intelligence · Computer Science 2017-11-16 Patrick Rodler , Wolfgang Schmid , Konstantin Schekotihin

We consider the problem of detecting an odd process among a group of Poisson point processes, all having the same rate except the odd process. The actual rates of the odd and non-odd processes are unknown to the decision maker. We consider…

Information Theory · Computer Science 2015-09-24 Nidhin Koshy Vaidhiyan , Rajesh Sundaresan

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…

Statistics Theory · Mathematics 2020-10-26 Michael Fauss , Abdelhak M. Zoubir , H. Vincent Poor

The problem of sequential detection of anomalies in multimodal data is considered. The objective is to observe physical sensor data from CCTV cameras, and social media data from Twitter and Instagram to detect anomalous behaviors or events.…

Applications · Statistics 2018-03-28 Taposh Banerjee , Gene Whipps , Prudhvi Gurram , Vahid Tarokh

Anomaly detection is a longstanding and active research area that has many applications in domains such as finance, security, and manufacturing. However, the efficiency and performance of anomaly detection algorithms are challenged by the…

Machine Learning · Computer Science 2025-04-16 Yang Cao , Haolong Xiang , Hang Zhang , Ye Zhu , Kai Ming Ting

Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with…

Methodology · Statistics 2025-12-18 Ivo V. Stoepker , Rui M. Castro , Ery Arias-Castro , Edwin van den Heuvel

A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests…

Statistics Theory · Mathematics 2009-09-29 Jay Bartroff

Clinical decision-making often involves selecting tests that are costly, invasive, or time-consuming, motivating individualized, sequential strategies for what to measure and when to stop ascertaining. We study the problem of learning…

Machine Learning · Statistics 2026-04-16 Doudou Zhou , Yiran Zhang , Dian Jin , Yingye Zheng , Lu Tian , Tianxi Cai

Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…

Probability · Mathematics 2021-03-03 Sugata Ghosh , Asok K. Nanda

Time series anomaly detection is crucial for industrial monitoring services that handle a large volume of data, aiming to ensure reliability and optimize system performance. Existing methods often require extensive labeled resources and…

Machine Learning · Computer Science 2023-07-21 Manqing Dong , Zhanxiang Zhao , Yitong Geng , Wentao Li , Wei Wang , Huai Jiang

Anomaly detection systems need to consider a lot of information when scanning for anomalies. One example is the context of the process in which an anomaly might occur, because anomalies for one process might not be anomalies for a different…

Machine Learning · Computer Science 2021-01-18 Sebastian Eresheim , Lukas Daniel Klausner , Patrick Kochberger

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

Statistics Theory · Mathematics 2022-07-04 Teppei Ogihara

While variable selection is essential to optimize the learning complexity by prioritizing features, automating the selection process is preferred since it requires laborious efforts with intensive analysis otherwise. However, it is not an…

Machine Learning · Computer Science 2019-10-29 Makiya Nakashima , Alex Sim , Youngsoo Kim , Jonghyun Kim , Jinoh Kim