Online Method for Updating Hyper-parameter of Gaussian Process
Seli Siti Sholihat (a), Sapto Wahyu Indratno(b,c*), Utriweni Mukhaiyar(b)

(a) Universitas Gunadarma, Depok, Indonesia
(b) Statistics Research Division, Institut Teknologi Bandung, Bandung, West Java, Indonesia
(c) University Center of Excellence on Artificial Intelligence for Vision, Natural Language Processing & Big Data Analytics (U-CoE AI-VLB), Institut Teknologi Bandung, Bandung, West Java, Indonesia
* sapto[at]math.itb.ac.id

Abstract

Abstract: Updating hyper-parameters is one of the exciting topics in the online Gaussian process for dynamic data structure. The covariance matrix size of the multivariate normal distribution in online Gaussian process increases as new data arrives. The challenge is the covariance matrix^s inversion, which gradually increases in size as the data comes. Inversion of covariance matrix in large size has high complexity. An iterative inversion of the covariance matrix solved the inversion problem and dynamic data structure. The method has less time computation and complexity rather than a direct inversion. Meanwhile, the covariance matrix in iterative inversion is defined by a fixed hyper-parameter that not suitable for dynamic data structure. The authors propose an online scheme for updating the Gaussian process^s hyper-parameters by combining the iterative covariance inversion and dynamic hyper-parameter. In dynamic hyper-parameters, the updating hyper-parameters use the maximum log-likelihood method. The online process offers an efficient and reliable method. The method is applied to the stock prices dataset. The results show that Gaussian process predictions perform well using the dynamic hyper-parameter into the iterative covariance inversion. The Root Mean Square Error (RMSE) in predicting stock prices using Gaussian process with an updated dynamic hyper-parameter is less than the RMSE using a fixed hyper-parameter (without updating).

Keywords: Online Gaussian process- Updating hyper-parameter- Iterative covariance matrix inversion

Topic: MATHEMATICS AND STATISTICS