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The scan statistic is by far the most popular method for anomaly detection, being popular in syndromic surveillance, signal and image processing, and target detection based on sensor networks, among other applications. The use of the scan…

Methodology · Statistics 2016-11-28 Ery Arias-Castro , Rui M. Castro , Ervin Tánczos , Meng Wang

We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…

Statistics Theory · Mathematics 2025-01-14 Chanwoo Lee , Miaoyan Wang

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Machine Learning · Computer Science 2020-07-09 Koji Maruhashi , Heewon Park , Rui Yamaguchi , Satoru Miyano

Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…

Machine Learning · Statistics 2026-04-28 Teruyuki Katsuoka , Tomohiro Shiraishi , Daiki Miwa , Vo Nguyen Le Duy , Ichiro Takeuchi

Multiview latent-variable models provide a fundamental framework for discrete data analysis, with applications to latent structure models, topic models, and mixtures of product distributions. In the discrete setting, the joint distribution…

Methodology · Statistics 2026-05-26 Runshi Tang , Julien Chhor , Olga Klopp , Alexandre B. Tsybakov , Anru R. Zhang

Tables are an abundant form of data with use cases across all scientific fields. Real-world datasets often contain anomalous samples that can negatively affect downstream analysis. In this work, we only assume access to contaminated data…

Machine Learning · Computer Science 2023-07-25 Guy Zamberg , Moshe Salhov , Ofir Lindenbaum , Amir Averbuch

Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel…

Machine Learning · Computer Science 2023-05-26 Hongzuo Xu , Yijie Wang , Juhui Wei , Songlei Jian , Yizhou Li , Ning Liu

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

Machine Learning · Statistics 2022-06-16 José Henrique de Morais Goulart , Romain Couillet , Pierre Comon

We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and…

Statistics Theory · Mathematics 2015-10-14 Hock Peng Chan , Guenther Walther

Anomaly detection aims at identifying data points that show systematic deviations from the majority of data in an unlabeled dataset. A common assumption is that clean training data (free of anomalies) is available, which is often violated…

Machine Learning · Computer Science 2022-07-20 Chen Qiu , Aodong Li , Marius Kloft , Maja Rudolph , Stephan Mandt

We are given a set of $n$ points that might be uniformly distributed in the unit square $[0,1]^2$. We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled…

Statistics Theory · Mathematics 2007-06-13 Ery Arias-Castro , David L. Donoho , Xiaoming Huo

Most of the existing methods for anomaly detection use only positive data to learn the data distribution, thus they usually need a pre-defined threshold at the detection stage to determine whether a test instance is an outlier.…

Machine Learning · Computer Science 2019-03-19 Kai Tian , Shuigeng Zhou , Jianping Fan , Jihong Guan

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

Anomaly detection is a crucial task in various domains. Most of the existing methods assume the normal sample data clusters around a single central prototype while the real data may consist of multiple categories or subgroups. In addition,…

Machine Learning · Statistics 2024-12-03 Zhijin Dong , Hongzhi Liu , Boyuan Ren , Weimin Xiong , Zhonghai Wu

In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be…

Machine Learning · Computer Science 2025-09-19 Padmaksha Roy , Almuatazbellah Boker , Lamine Mili

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…

Mesoscale and Nanoscale Physics · Physics 2021-03-19 Yuan Yang , Jie Ding

Many organisations manage service quality and monitor a large set devices and servers where each entity is associated with telemetry or physical sensor data series. Recently, various methods have been proposed to detect behavioural…

Social and Information Networks · Computer Science 2023-05-10 Len Feremans , Boris Cule , Bart Goethals

Anomaly detection is the process of finding data points that deviate from a baseline. In a real-life setting, anomalies are usually unknown or extremely rare. Moreover, the detection must be accomplished in a timely manner or the risk of…

Machine Learning · Computer Science 2019-04-26 Mariem Ben Fadhel , Kofi Nyarko

We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…

Applications · Statistics 2013-12-02 Mikhail Langovoy , Michael Habeck , Bernhard Schölkopf

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Machine Learning · Computer Science 2016-06-13 Furong Huang