Sequential anomaly detection in the presence of noise and limited feedback

Maxim Raginsky, Rebecca M. Willett, Corinne Horn, Jorge Silva, Roummel F. Marcia

Research output: Contribution to journalArticlepeer-review


This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: 1) filtering, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations and 2) hedging, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset.

Original languageEnglish (US)
Article number6208875
Pages (from-to)5544-5562
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - 2012


  • Anomaly detection
  • exponential families
  • filtering
  • individual sequences
  • label-efficient prediction
  • minimax regret
  • online convex programming (OCP)
  • prediction with limited feedback
  • sequential probability assignment
  • universal prediction

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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