Detecting gradual changes from data stream using MDL-change statistics

In this paper we propose a novel methodology of sequential change detection using the minimum description length (MDL)-change statistics. We first introduce the MDL-change statistics as the difference between the code-lengths with change and that without change. We give a theoretical justification for its use in the scenario of hypothesis testing. In it we evaluate the error probabilities for the MDL-change detection to relate them to the information-theoretic complexities of the probabilistic models and their discrepancy measure. We then convert the MDL-change statistics into the sequential change detection algorithm. It is designed to detect gradual changes as well as abrupt changes from big stream data. We empirically demonstrate the effectiveness of the proposed method by showing that it performs better than existing algorithms for synthetic data. We also show its validity through real problems such as SQL injection detection and failure symptom detection.