ONLINE CHANGE POINT DETECTION ON TIME SERIES USING ITERATIVE GAUSSIAN PROCESS METHOD - Siti Sholihat, Seli
Development of the internet affects humans on obtaining data by online, including time series can be taken in real-time so then built a dynamic data structure (data size grows). The problem of finding changes in data when the property of the time series changes is called change point detection (CPD). CPD is useful for control processes and prevention losses in financial/economic, health, or social. Some of CPD methods include the Bayesian method, bootstrap, variational, fuzzy statistics, Bayesian Online Changepoint detection (BOCPD) for exponential family, and BOCPD method for Gaussian process. One of the CPD methods that can be used for dynamic data structure is BOCDP method. BOCPD at first is defined for data that comes from exponential family with the independent and identically distributed random variables assumption. The online formula for updating parameters of distribution uses the conjugate exponential formula. Next, Gaussian process in BOCPD is developed with dependencies random variables assumption. However, the application Gaussian process in BOCPD is not efficient because using direct inversion of covariance matrix and hyper-parameters marginalization by integrals that are difficult to solve precisely. Therefore, online scheme of Gaussian process for BOCDP is needed. The research developed iterative Gaussian process for efficient online scheme of Gaussian process in BOCPD. The iterative Gaussian process is developed using two main ideas, iterative covariance matrix inversion and maximum Log-likelihood method. The iterative inversion method has less complexity than direct inversion method (inversion from the original matrix). This iterative inversion method can be used to perform an efficient inversion of covariance matrix as new data arrives. The iterative covariance matrix inversion uses the assumption of a fixed hyper-parameter in the covariance matrix over time without updating the hyper-parameters. We define the covariance matrix with dynamic hyper-parameters to build the mathematical form of iterative inversion so then the hyper-parameters of Gaussian process can be updated. The updating hyper-parameters are determined using maximum Log-likelihood method, Log-likelihood that apply iterative inversion. Iterative Gaussian process for BOCPD offers an efficient online scheme with dynamic hyper-parameter updating based on the new data coming. These updating hyper-parameter gives an accurate gaussian process. It can be seen on Root Mean Square Error (RMSE) of Gaussian process predictions by updating dynamic hyper-parameter is less than using fixed hyper-parameter. It shows that the iterative Gaussian process performs well in prediction. BOCPD with iterative Gaussian process detects change of time series with 82.5% accuracy.