Online Inverse Covariance Matrix: In Application to Predictive Distribution of Gaussian Process

Some statistical analysis needs an inverse covariance matrix computing. A Gaussian process is a non-parametric method in statistical analysis that has been applied to some research. The Gaussian process needs an inverse covariance matrix computing by given data. Inverse matrix on Gaussian process becomes interesting problems in Gaussian process when it is applied in real time and have big number data. Increasing data number and covariance matrix size need an effective computing algorithm. Some online Gaussian process is developed to solve those real-time cases and increasing of covariance matrix size. Here, we discuss how online Gaussian process is built from an online algorithm of inverse covariance matrix. We do simulation online inverse covariance matrix for efficient time-computing of Gaussian process predictive distribution. We compare performance of online inverse covariance matrix and offline inverse covariance matrix to predictive distribution of Gaussian process. The result shows that time-computing online inverse covariance matrices are faster than offline. Meanwhile, the online inversion to Gaussian process shows that predictive Gaussian processes have the same root mean square error (RMSE) compare to offline inversion. It means that inversion by online affects time-computing, but still the predictive distribution of Gaussian process is preserved.