Modified approach towards gaussian process regression based on incremental learning

Abstract

This research propounds a variant of Gaussian process regression called Sparse Incremental Gaussian Process Regression (si-GPR).Traditional Gaussian process regression, although attractive for smaller datasets, possesses some inherent limitations regarding computation and storage requirements. As a result, traditional or batch-GPR performs poorly when employed for training a large set of data. Again, this algorithm can neither accommodate inputs that become available over time nor the training set that needs the removal of training points. Therefore, appropriate methods are necessitated to deal with these limitations effectively. To accomplish that, a sparse Gaussian process regression algorithm with an incremental learning and a decremental un-learning policy has been proposed. In this formulation, the idea of sparsification and undertaking streaming inputs has been merged with the provision of model forgetting. The rationale behind following this strategy is three-fold: to lessen the number of data instances to fit, to accommodate streaming input, and to minimize the computation and memory requirements as possible. As the prime aspiration was to lower the calculations without losing the accuracy, an economic update of the kernel matrix and the inverted lower Cholesky matrix has been rendered. The outcome of this research manifests promising results as it provides a general reduction in memory consumption and execution time. Moreover, the proposed si-GPR algorithm provides better fitting and predictions over the original Gaussian process regression.