  An extremely common bottleneck encountered in statistical learning algorithms
is inversion of huge covariance matrices, examples being in evaluating Gaussian
likelihoods for a large number of data points. We propose general parallel
algorithms for inverting positive definite matrices, which are nearly rank
deficient. Such matrix inversions are needed in Gaussian process computations,
among other settings, and remain a bottleneck even with the increasing
literature on low rank approximations. We propose a general class of algorithms
for parallelizing computations to dramatically speed up computation time by
orders of magnitude exploiting multicore architectures. We implement our
algorithm on a cloud computing platform, providing pseudo and actual code. The
algorithm can be easily implemented on any multicore parallel computing
resource. Some illustrations are provided to give a flavor for the gains and
what becomes possible in freeing up this bottleneck.
