Decomposition of Event Sequences into Independent Components

Many real-world processes result in an extensive logs of sequences of events, i.e., events coupled with time of occurrence. Examples of such process logs include alarms produced by a large telecommunication network, web-access data, biostatistics, etc. In many cases, it is useful to decompose the incoming stream of events into the number of independent streams. Such decomposition may reveal valuable information about the event generating process, e.g. dependencies among alarms in the telecommunication network, relationships between web-users and relevant symptoms of the decease. It may, as well, facilitate further analysis of the data by working with independent components separately. In this paper we describe a theoretical framework and practical methods for finding event sequence decompositions. These methods use the probabilistic modeling of the event generating process. The probabilistic model predicts (with given confidence) the range of observed statistics for the independent subsequence event generation processes. The predicted values are used to determine the independence relations among the event types in the observed sequence of events, and these relations are used to decompose the sequences. The presented techniques were validated by analyzing real data from a telecommunication network and on synthetic data that was generated under two different models. In the first dataset, the a priori event distribution was uniform, and in the second dataset events have followed a predefined burst-type a priori distribu-