Covariance matrix estimation for multivariate Gaussian process regression

松村 祐貴, 和田 俊和

Gaussian process regression is a nonlinear regression that estimates the expected value of the of the output and its variance for given input. The original Gaussian process regression estimates a scalar value as an expected value of output, which can simply be extended to estimate a vector value. However, the covariance matrix cannot be estimated by simple extension. We have proposed an accelerated Gaussian process regression by introducing dynamic active set consisting of input-output pairs, and the weighted output covariance can be utilized as the covariance of output for multivariate Gaussian process regression. However, the diagonal elements of the estimated matrix can be negative. This is caused by the negative weight of the outputs originated by the inverse of gram matrix. In this report, we propose a method to estimate non-negative weights for the outputs. The estimation is twofold: initially estimate the output vector by simple multivariate Gaussian process regression, then recompute non-negative weights so as to minimize the output error. The resulted weights are utilized to estimate covariance matrix. By using the proposed method in anomaly detection of plant data and electrocardiogram data in the experiment, it was confirmed its effectiveness.

Covariance matrix estimation for multivariate Gaussian process regression

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