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.
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