Bayesian localization of anomaly in distributed networks with quadratic criterion

The anomaly localization in distributed networks can be treated as a multiple hypothesis testing (MHT) problem and the Bayesian test with 0-1 loss function is a standard solution to this problem. However, For the anomaly localization application, the cost of different false localization varies, which cannot be reflected by the 0 - 1 loss function while the quadratic loss function is more appropriate. The main contribution of the paper is the design of a Bayesian test with a quadratic loss function and its performance analysis. The non-asymptotic bounds of the misclassification probabilities of the proposed test and the standard one with 0-1 loss function are established and the relationship between their asymptotic equivalence with respect to signal-to-noise ratio and the geometry of the parameter space is analyzed. The effectiveness of the non-asymptotic bounds and the analysis on the asymptotic equivalence are verified by the simulation results.

[1]  George V. Moustakides,et al.  Detection and diagnosis of changes in the eigenstructure of nonstationary multivariable systems , 1987, Autom..

[2]  VARUN CHANDOLA,et al.  Anomaly detection: A survey , 2009, CSUR.

[3]  Lionel Fillatre.  Adaptive Steganalysis of Least Significant Bit Replacement in Grayscale Natural Images , 2012, IEEE Transactions on Signal Processing.

[4]  Mitra Fouladirad,et al.  Optimal statistical fault detection with nuisance parameters , 2005, Autom..

[5]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[6]  Hongliang Fei,et al.  Anomaly localization for network data streams with graph joint sparse PCA , 2011, KDD.

[7]  Mikhail J. Atallah,et al.  Reliable detection of episodes in event sequences , 2004, Knowledge and Information Systems.

[8]  Simon J. Godsill,et al.  Detection of abrupt spectral changes using support vector machines an application to audio signal segmentation , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  Alfred O. Hero,et al.  Optimal simultaneous detection and estimation under a false alarm constraint , 1995, IEEE Trans. Inf. Theory.

[10]  S. Holm.  A Simple Sequentially Rejective Multiple Test Procedure , 1979 .

[11]  Ashish Mishra,et al.  Detecting border intrusion using wireless sensor network and artificial neural network , 2010, 2010 6th IEEE International Conference on Distributed Computing in Sensor Systems Workshops (DCOSSW).

[12]  Jian Zhang,et al.  Bayesian Test for Multiple Hypothesis Testing Problem with Quadratic Loss , 2013, ALCOSP.

[13]  Igor V. Nikiforov,et al.  Asymptotically Uniformly Minimax Detection and Isolation in Network Monitoring , 2012, IEEE Transactions on Signal Processing.