Abstract
In this paper, we study a problem of anomaly
detection from time series-data.We propose to use kernel
quantile regression (KQR) that can predict the extreme quantiles such
as 0.01 or 0.99 quantiles (1 or 99 percentile) of conditional distributions. Using the KQR, we can tell whether the probability of observing a certain time-series sequence is larger than, say, 1 percent or not. This information can be used to tell whether there is an anomaly or not. An important aspect of the methodology used in time-series analyses is its adaptability. In this paper, to adapt the KQR in on-line manner, we develop an efficient update algorithm of KQR. In particular, the proposed new algorithm 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.
