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We present a method for a reliable detection of "unusual" † The work of this author was supported by the NSF Grant CCR-0208709, and NIH grant R01 GM068959-01.‡ The work of this author was supported by the NSF Grant CCR-0208709, and AFOSR Grant FA 8655-04-1-3074.but did not consider more than one episode scanned simultaneously for an occurrence.

We propose a new method for a reliable identification of significant sequential episodes occurring within a window of size w in an event sequence modeled by a Markov source. As a measure of significance we use Ω ∃ (n, w), the number of windows containing the episode as a subsequence. We prove that Ω ∃ (n, w) is a sum of a ϕ-mixing sequence of random variables and therefore obeys the central limit theorem. This leads us to a computational formula for a threshold to identify significant episodes. The novelty of our method for Markov source stems from the fact that, instead of scoring the whole sequence using a Markov model, we compute the expected value of Ω ∃ (n, w) and its variance in order to estimate the threshold and compare it to the observed Ω ∃ (n, w). Since performance of the method critically depends on the model structure and parameters, we argue that variable-length Markov models of event streams are superior to fixed-length Markov models. We chose DNA sequences as event sources in experiments, and compared the performance of fixed-length Markov models with interpolated Markov models. This paper is an extension of our previous work in [8, 1] where we considered the problem of the reliable detection of significant episodes for memoryless sources.

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