Adaptive Kernel Quantile Regression for Anomaly Detection
Hiroyuki Moriguchi*, Ichiro Takeuchi**,
Masayuki Karasuyama**, Shin-ichi Horikawa*,
Yoshikatsu Ohta*, Tetsuji Kodama* and Hiroshi Naruse*
* Mie University, 1577 Kurimamachiya-cho, Tsu, Mie 514-8507, Japan
** Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
In this paper, we study a problem of anomaly detection from time series-data. We use kernel quantile regression (KQR) to predict the extreme (such as 0.01 or 0.99) quantiles of the future time-series data distribution. It enables us to tell whether the probability of observing a certain time-series sequence is larger than, say, 1 percent or not. In this paper, we develop an efficient update algorithm of KQR in order to adapt the KQR in on-line manner. We propose a new algorithm that allows us to compute the optimal solution of the KQR when a new training pattern is inserted or deleted. We demonstrate the effectiveness of our methodology through numerical experiment using real-world time-series data.
Masayuki Karasuyama, Shin-ichi Horikawa,
Yoshikatsu Ohta, Tetsuji Kodama, and Hiroshi Naruse, “Adaptive Kernel Quantile Regression for Anomaly Detection,” J. Adv. Comput. Intell. Intell. Inform., Vol.13, No.3, pp. 230-236, 2009.
-  J. D. Hamilton, “Time series analysis,” Princeton University Press, 1994.
-  R. Engle, “Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflations,” Econometrica, Vol.50, pp. 987-1008, 1982.
-  R. Koenker and G. Bassett, “Regression quantiles,” Econometrica, Vol.46, No.1, pp. 33-50, 1978.
-  I. Takeuchi, Q. V. Le, T. Sears, and A. J. Smola, “Nonparametric quantile estimation,” Journal of Machine Learning Research, Vol.7, pp. 1231-1264, 2006.
-  G. Cauwenberghs and T. Poggio, “Incremental and decremental support vector machine learning,” In Advances in Neural Information Processing Systems, Vol.13, pp. 409-415, 2001.
-  J. Ma, J. Theiler, and S. Perkins, “Accurate on-line support vector regression,” Neural Computation, Vol.15, No.11, pp. 2683-2703, 2003.
-  I. Takeuchi, K. Nomura, and T. Kanamori, “Nonparametric conditional density estimation using piecewise-linear solution path of kernel quantile regression,” Neural Computation, Vol.21, No.2, pp. 533-559, 2009.
-  R. Horn and C. R. Johnson, “Matrix analysis,” Cambridge University Press, 1985.
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