• About
  • Policies
  • What is openaccess
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Engineering
      • Department of Electrical and Electronics Engineering
      • View Item
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Engineering
      • Department of Electrical and Electronics Engineering
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Online anomaly detection with minimax optimal density estimation in nonstationary environments

      Thumbnail
      View / Download
      1.4 Mb
      Author
      Gokcesu, K.
      Kozat, S. S.
      Date
      2018
      Source Title
      IEEE Transactions on Signal Processing
      Print ISSN
      1053-587X
      Publisher
      Institute of Electrical and Electronics Engineers
      Volume
      66
      Issue
      5
      Pages
      1213 - 1227
      Language
      English
      Type
      Article
      Item Usage Stats
      109
      views
      152
      downloads
      Abstract
      We introduce a truly online anomaly detection algorithm that sequentially processes data to detect anomalies in time series. In anomaly detection, while the anomalous data are arbitrary, the normal data have similarities and generally conforms to a particular model. However, the particular model that generates the normal data is generally unknown (even nonstationary) and needs to be learned sequentially. Therefore, a two stage approach is needed, where in the first stage, we construct a probability density function to model the normal data in the time series. Then, in the second stage, we threshold the density estimation of the newly observed data to detect anomalies. We approach this problem from an information theoretic perspective and propose minimax optimal schemes for both stages to create an optimal anomaly detection algorithm in a strong deterministic sense. To this end, for the first stage, we introduce a completely online density estimation algorithm that is minimax optimal with respect to the log-loss and achieves Merhav's lower bound for general nonstationary exponential-family of distributions without any assumptions on the observation sequence. For the second stage, we propose a threshold selection scheme that is minimax optimal (with logarithmic performance bounds) against the best threshold chosen in hindsight with respect to the surrogate logistic loss. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art density estimation based anomaly detection algorithms in the literature.
      Keywords
      Anomaly detection
      Density estimation
      Minimax optimal
      Online learning
      Time series
      Permalink
      http://hdl.handle.net/11693/50286
      Published Version (Please cite this version)
      https://doi.org/10.1109/TSP.2017.2784390
      Collections
      • Department of Electrical and Electronics Engineering 3605
      Show full item record

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartments

      My Account

      Login

      Statistics

      View Usage StatisticsView Google Analytics Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the site administrator. Phone: (312) 290 1771
      © Bilkent University - Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin | Privacy