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Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that…

Machine Learning · Statistics 2021-08-12 Christian Brownlees , Jordi Llorens-Terrazas

Detecting anomalies in time series data is important in a variety of fields, including system monitoring, healthcare, and cybersecurity. While the abundance of available methods makes it difficult to choose the most appropriate method for a…

Machine Learning · Computer Science 2023-02-03 Ferdinand Rewicki , Joachim Denzler , Julia Niebling

Time series forecasting is an important and forefront task in many real-world applications. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since…

Machine Learning · Computer Science 2024-02-06 Hao Cheng , Qingsong Wen , Yang Liu , Liang Sun

Time series anomaly detection has been a perennially important topic in data science, with papers dating back to the 1950s. However, in recent years there has been an explosion of interest in this topic, much of it driven by the success of…

Machine Learning · Computer Science 2022-09-07 Renjie Wu , Eamonn J. Keogh

Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for…

Machine Learning · Statistics 2021-04-19 Andrew R. Lawrence , Marcus Kaiser , Rui Sampaio , Maksim Sipos

A major concern when dealing with financial time series involving a wide variety ofmarket risk factors is the presence of anomalies. These induce a miscalibration of the models used toquantify and manage risk, resulting in potential…

Statistical Finance · Quantitative Finance 2022-10-26 Stéphane Crépey , Lehdili Noureddine , Nisrine Madhar , Maud Thomas

Anomaly detection to recognize unusual events in large scale systems in a time sensitive manner is critical in many industries, eg. bank fraud, enterprise systems, medical alerts, etc. Large-scale systems often grow in size and complexity…

Machine Learning · Computer Science 2022-10-31 Srishti Mishra , Tvarita Jain , Dinkar Sitaram

Large companies need to monitor various metrics (for example, Page Views and Revenue) of their applications and services in real time. At Microsoft, we develop a time-series anomaly detection service which helps customers to monitor the…

Machine Learning · Computer Science 2019-06-11 Hansheng Ren , Bixiong Xu , Yujing Wang , Chao Yi , Congrui Huang , Xiaoyu Kou , Tony Xing , Mao Yang , Jie Tong , Qi Zhang

Despite the prevalence of reconstruction-based deep learning methods, time series anomaly detection remains a tremendous challenge. Existing approaches often struggle with limited temporal contexts, insufficient representation of normal…

Machine Learning · Computer Science 2025-07-16 Zhijie Zhong , Zhiwen Yu , Xing Xi , Yue Xu , Wenming Cao , Yiyuan Yang , Kaixiang Yang , Jane You

Deep neural networks are known to be vulnerable to unseen data: they may wrongly assign high confidence stcores to out-distribuion samples. Recent works try to solve the problem using representation learning methods and specific metrics. In…

Computer Vision and Pattern Recognition · Computer Science 2022-06-07 Haowei He , Jiaye Teng , Yang Yuan

We apply several machine learning algorithms to the problem of anomaly detection in operational data for large-scale, high-voltage electric power grids. We observe important differences in the performance of the algorithms. Neural networks…

Systems and Control · Electrical Eng. & Systems 2026-02-12 Marc Gillioz , Guillaume Dubuis , Étienne Voutaz , Philippe Jacquod

Time series anomaly detection is important in modern large-scale systems and is applied in a variety of domains to analyze and monitor the operation of diverse systems. Unsupervised approaches have received widespread interest, as they do…

Machine Learning · Computer Science 2025-10-23 Buang Zhang , Tung Kieu , Xiangfei Qiu , Chenjuan Guo , Jilin Hu , Aoying Zhou , Christian S. Jensen , Bin Yang

Time-series anomaly detection is critical for ensuring safety in high-stakes applications, where robustness is a fundamental requirement rather than a mere performance metric. Addressing the vulnerability of these systems to adversarial…

Machine Learning · Computer Science 2026-05-11 Shijie Liu , Tansu Alpcan , Christopher Leckie , Sarah Erfani

The ability to quickly and accurately detect anomalous structure within data sequences is an inference challenge of growing importance. This work extends recently proposed post-hoc (offline) anomaly detection methodology to the sequential…

Methodology · Statistics 2020-09-16 Alexander T. M. Fisch , Lawrence Bardwell , Idris A. Eckley

Given a black-box classification model and an unlabeled evaluation dataset from some application domain, efficient strategies need to be developed to evaluate the model. Random sampling allows a user to estimate metrics like accuracy,…

Machine Learning · Computer Science 2021-02-26 Walter Bennette , Sally Dufek , Karsten Maurer , Sean Sisti , Bunyod Tusmatov

One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that…

Machine Learning · Computer Science 2020-11-03 Ilja Kuzborskij , Nicolò Cesa-Bianchi

It has been shown that deep learning models can under certain circumstances outperform traditional statistical methods at forecasting. Furthermore, various techniques have been developed for quantifying the forecast uncertainty (prediction…

Machine Learning · Computer Science 2021-10-08 Thabang Mathonsi , Terence L. van Zyl

Time series anomalies can offer information relevant to critical situations facing various fields, from finance and aerospace to the IT, security, and medical domains. However, detecting anomalies in time series data is particularly…

Machine Learning · Computer Science 2020-11-17 Alexander Geiger , Dongyu Liu , Sarah Alnegheimish , Alfredo Cuesta-Infante , Kalyan Veeramachaneni

Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at both forecasting tasks, and at quantifying the uncertainty associated with those forecasts (prediction intervals). One example is Multivariate…

Machine Learning · Computer Science 2022-02-28 Thabang Mathonsi , Terence L van Zyl

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

Methodology · Statistics 2021-06-11 Darren Homrighausen , Daniel J. McDonald
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