Approximating Gaussian Processes with H2-Matrices

To compute the exact solution of Gaussian process regression one needs O(N) computations for direct and O(N) for iterative methods since it involves a densely populated kernel matrix of size N×N , here N denotes the number of data. This makes large scale learning problems intractable by standard techniques. We propose to use an alternative approach: the kernel matrix is replaced by a data-sparse approximation, called an H-matrix. This matrix can be represented by only O(Nm) units of storage, where m is a parameter controlling the accuracy of the approximation, while the computation of the H-matrix scales with O(Nm logN). Practical experiments demonstrate that our scheme leads to significant reductions in storage requirements and computing times for large data sets in lower dimensional spaces.