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Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

Machine Learning · Statistics 2026-05-05 Sebastian Engelke , Nicola Gnecco , Anne Sabourin

One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…

Probability · Mathematics 2007-05-23 Laurent Gardes , Stephane Girard

Anomaly detection is crucial for understanding unusual behaviors in data, as anomalies offer valuable insights. This paper introduces Dependency-based Anomaly Detection (DepAD), a general framework that utilizes variable dependencies to…

Machine Learning · Computer Science 2024-04-18 Sha Lu , Lin Liu , Kui Yu , Thuc Duy Le , Jixue Liu , Jiuyong Li

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

Estimating the probability of rare channel conditions is a central challenge in ultra-reliable wireless communication, where random events, such as deep fades, can cause sudden variations in the channel quality. This paper proposes a…

Signal Processing · Electrical Eng. & Systems 2024-07-08 Tobias Kallehauge , Anders E. Kalør , Pablo Ramírez-Espinosa , Christophe Biscio , Petar Popovski

Anomaly detection involves identifying instances within a dataset that deviate from the norm and occur infrequently. Current benchmarks tend to favor methods biased towards low diversity in normal data, which does not align with real-world…

Computer Vision and Pattern Recognition · Computer Science 2024-06-18 Mohammad Akhavan Anvari , Rojina Kashefi , Vahid Reza Khazaie , Mohammad Khalooei , Mohammad Sabokrou

Anomalies are those deviating from the norm. Unsupervised anomaly detection often translates to identifying low density regions. Major problems arise when data is high-dimensional and mixed of discrete and continuous attributes. We propose…

Machine Learning · Computer Science 2016-10-21 Kien Do , Truyen Tran , Svetha Venkatesh

In anomaly detection, a prominent task is to induce a model to identify anomalies learned solely based on normal data. Generally, one is interested in finding an anomaly detector that correctly identifies anomalies, i.e., data points that…

Machine Learning · Computer Science 2022-11-28 David Schubert , Pritha Gupta , Marcel Wever

Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise…

Statistics Theory · Mathematics 2021-05-20 Mads Lindskou , Torben Tvedebrink , Poul Svante Eriksen , Niels Morling

Anomaly detection aims to detect data that do not conform to regular patterns, and such data is also called outliers. The anomalies to be detected are often tiny in proportion, containing crucial information, and are suitable for…

Machine Learning · Computer Science 2023-06-06 Fan Xu , Nan Wang , Xibin Zhao

We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We…

Statistics Theory · Mathematics 2011-03-10 Ery Arias-Castro , Emmanuel J. Candès , Arnaud Durand

Extreme value theory (EVT) is a statistical tool for analysis of extreme events. It has a strong theoretical background, however, we need to choose hyper-parameters to apply EVT. In recent studies of machine learning, techniques of choosing…

Machine Learning · Computer Science 2021-07-14 Chikara Nakamura

We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…

Statistics Theory · Mathematics 2023-04-12 Surya T. Tokdar , Ryan Martin

The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…

Information Theory · Computer Science 2020-04-22 Bar Hemo , Tomer Gafni , Kobi Cohen , Qing Zhao

We propose two robust methods for anomaly detection in dynamic networks in which the properties of normal traffic are time-varying. We formulate the robust anomaly detection problem as a binary composite hypothesis testing problem and…

Networking and Internet Architecture · Computer Science 2015-03-10 Jing Wang , Ioannis Ch. Paschalidis

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…

Machine Learning · Computer Science 2012-09-27 Ruefei He , Jonathan Shapiro

KPI anomaly detection is one important function of network management system. Traditional methods either require prior knowledge or manually set thresholds. To overcome these shortcomings, we propose the Ensemble2 framework, which applies…

Machine Learning · Computer Science 2022-06-01 Shi-Yang Wang

Extreme value analysis for time series is often based on the block maxima method, in particular for environmental applications. In the classical univariate case, the latter is based on fitting an extreme-value distribution to the sample of…

Statistics Theory · Mathematics 2026-04-20 Axel Bücher , Erik Haufs

Time series models often deal with extreme events and anomalies, both prevalent in real-world datasets. Such models often need to provide careful probabilistic forecasting, which is vital in risk management for extreme events such as…

Machine Learning · Statistics 2022-08-23 Ashkan Farhangi , Jiang Bian , Arthur Huang , Haoyi Xiong , Jun Wang , Zhishan Guo

Anomaly detection is a method for discovering unusual and suspicious behavior. In many real-world scenarios, the examined events can be directly linked to the actions of an adversary, such as attacks on computer networks or frauds in…

Machine Learning · Computer Science 2020-04-23 Olga Petrova , Karel Durkota , Galina Alperovich , Karel Horak , Michal Najman , Branislav Bosansky , Viliam Lisy