Change Point Detection in Piece-wise Stationary Time Series
Stationarity is a fundamental prerequisite in time-series analysis. However, real-world time series from diverse domains often exhibit non-stationarity. Examples include but are not limited to finance, neuroscience, and social networks. One significant subset of non-stationary time series is piece-wise stationary time series, characterized by abrupt distributional changes at specific time points, dividing the series into stationary segments. This work focuses on the challenging task of change point detection (CPD) in piece-wise stationary time series.
This presentation comprises three key stages, all centered around CPD and piece-wise stationary time series. In the first stage, we introduce a novel CPD method that leverages clustering sliding windows and integer linear programming (ILP). Unlike existing methods that require extensive parameter tuning and rely on unrealistic statistical assumptions, our approach eliminates the need for user-defined thresholds and automatically determines the number of change points. Furthermore, it accommodates time-dependent data and various distributional changes.
In the second stage, we extend our efforts to efficiently detect multiple unknown change points in multivariate time series using a greedy search algorithm guided by the minimum description length principle. This method inherits the advantages of the ILP approach while addressing its scalability limitations. We provide a theoretical guarantee of our method's effectiveness.
In the third stage, we identify and solve a novel problem: Change point detection in continuous time. Building on the greedy method introduced in stage two, we present an unsupervised approach for detecting change points in continuous-time discrete-events sequences, addressing the challenge of identifying multiple change points in piecewise stationary point processes.
Throughout each stage, we conduct extensive experiments using both synthetic and real-world data to showcase the superior performance of our proposed methods.
Committee: Christopher Quinn (major professor), Pavan Aduri, Forest Bao, Hongyang Gao and Qing Li
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