  Standard Gaussian Process (GP) regression, a powerful machine learning tool,
is computationally expensive when it is applied to large datasets, and
potentially inaccurate when data points are sparsely distributed in a
high-dimensional feature space. To address these challenges, a new multiscale,
sparsified GP algorithm is formulated, with the goal of application to large
scientific computing datasets. In this approach, the data is partitioned into
clusters and the cluster centers are used to define a reduced training set,
resulting in an improvement over standard GPs in terms of training and
evaluation costs. Further, a hierarchical technique is used to adaptively map
the local covariance representation to the underlying sparsity of the feature
space, leading to improved prediction accuracy when the data distribution is
highly non-uniform. A theoretical investigation of the computational complexity
of the algorithm is presented. The efficacy of this method is then demonstrated
on smooth and discontinuous analytical functions and on data from a direct
numerical simulation of turbulent combustion.
