document: A unifying framework for detecting outliers and change points from non-stationary time series data We are concerned with the issues of outlier detection and change point detection from a data stream . In the area of data mining , there have been increased interest in these issues since the former is related to fraud detection , rare event discovery , etc. , while the latter is related to event\/trend by change detection , activity monitoring , etc. . Specifically , it is important to consider the situation where the data source is non-stationary , since the nature of data source may change over time in real applications . Although in most previous work outlier detection and change point detection have not been related explicitly , this paper presents a unifying framework for dealing with both of them on the basis of the theory of on-line learning of non-stationary time series . In this framework a probabilistic model of the data source is incrementally learned using an on-line discounting learning algorithm , which can track the changing data source adaptively by forgetting the effect of past data gradually . Then the score for any given data is calculated to measure its deviation from the learned model , with a higher score indicating a high possibility of being an outlier . Further change points in a data stream are detected by applying this scoring method into a time series of moving averaged losses for prediction using the learned model . Specifically we develop an efficient algorithms for on-line discounting learning of auto-regression models from time series data , and demonstrate the validity of our framework through simulation and experimental applications to stock market data analysis .
doc_bio_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O