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The anomaly detection problem for univariate or multivariate time series is a critical question in many practical applications as industrial processes control, biological measures, engine monitoring, supervision of all kinds of behavior. In…

Statistics Theory · Mathematics 2020-10-16 Marie Cottrell , Cynthia Faure , Jérôme Lacaille , Madalina Olteanu

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

Information Theory · Computer Science 2025-01-07 Ching-Fang Li , I-Hsiang Wang

Outlying observations, which significantly deviate from other measurements, may distort the conclusions of data analysis. Therefore, identifying outliers is one of the important problems that should be solved to obtain reliable results.…

Computation · Statistics 2014-05-01 Soo-Heang Eo , Seung-Mo Hong , HyungJun Cho

In a corpus of data, outliers are either errors: mistakes in the data that are counterproductive, or are unique: informative samples that improve model robustness. Identifying outliers can lead to better datasets by (1) removing noise in…

The following detection problem is studied, in which there are $M$ sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains $n$ independent and identically distributed (i.i.d.) continuous…

Information Theory · Computer Science 2015-10-08 Yuheng Bu , Shaofeng Zou , Yingbin Liang , Venugopal V. Veeravalli

The problem of sequentially detecting a moving anomaly which affects different parts of a sensor network with time is studied. Each network sensor is characterized by a non-anomalous and anomalous distribution, governing the generation of…

Statistics Theory · Mathematics 2020-07-30 Georgios Rovatsos , George V. Moustakides , Venugopal V. Veeravalli

This paper introduces a new methodology for detecting anomalies in time series data, with a primary application to monitoring the health of (micro-) services and cloud resources. The main novelty in our approach is that instead of modeling…

Machine Learning · Computer Science 2020-07-31 Fadhel Ayed , Lorenzo Stella , Tim Januschowski , Jan Gasthaus

We study the change detection problem with an unknown post-change distribution. Under this constraint, the unknown change in the distribution of observations may occur in many ways without much structure on the observations, whereas, before…

Signal Processing · Electrical Eng. & Systems 2020-12-11 Deniz Sargun , C. Emre Koksal

It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time.…

Methodology · Statistics 2015-05-08 Gordon J Ross

We propose a new outlier detection method for multi-dimensional data. The method detects outliers based on vector cosine similarity, using a new dataset constructed by adding a dimension with zero values to the original data. When a point…

Machine Learning · Computer Science 2026-01-06 Zhongyang Shen

We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…

Statistics Theory · Mathematics 2013-01-23 Georgios Fellouris , Alexander G. Tartakovsky

Several techniques for multivariate time series anomaly detection have been proposed recently, but a systematic comparison on a common set of datasets and metrics is lacking. This paper presents a systematic and comprehensive evaluation of…

Machine Learning · Computer Science 2021-09-24 Astha Garg , Wenyu Zhang , Jules Samaran , Savitha Ramasamy , Chuan-Sheng Foo

We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those…

Methodology · Statistics 2022-02-01 Ning Sun , Chen Yang , Ričardas Zitikis

This paper proposes a novel fast online methodology for outlier detection called the exception maximization outlier detection method(EMODM), which employs probabilistic models and statistical algorithms to detect abnormal patterns from the…

Machine Learning · Statistics 2025-06-03 Zhikun Zhang , Yiting Duan , Xiangjun Wang , Mingyuan Zhang

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…

Methodology · Statistics 2022-09-12 Zifeng Zhao , Feiyu Jiang , Xiaofeng Shao

Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the…

Machine Learning · Computer Science 2024-01-23 Dongmin Kim , Sunghyun Park , Jaegul Choo

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic.…

Logic in Computer Science · Computer Science 2016-02-09 Daisuke Ishii , Naoki Yonezaki , Alexandre Goldsztejn

Time series often contain outliers and level shifts or structural changes. These unexpected events are of the utmost importance in fraud detection, as they may pinpoint suspicious transactions. The presence of such unusual events can easily…

Computation · Statistics 2021-01-13 Peter J. Rousseeuw , Domenico Perrotta , Marco Riani , Mia Hubert

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

Sequential change-point detection for time series enables us to sequentially check the hypothesis that the model still holds as more and more data are observed. It is widely used in data monitoring in practice. In this work, we consider…

Methodology · Statistics 2025-09-10 Yajun Liu , Beth Andrews