  Gaussian process regression generally does not scale to beyond a few
thousands data points without applying some sort of kernel approximation
method. Most approximations focus on the high eigenvalue part of the spectrum
of the kernel matrix, $K$, which leads to bad performance when the length scale
of the kernel is small. In this paper we introduce Multiresolution Kernel
Approximation (MKA), the first true broad bandwidth kernel approximation
algorithm. Important points about MKA are that it is memory efficient, and it
is a direct method, which means that it also makes it easy to approximate
$K^{-1}$ and $\mathop{\textrm{det}}(K)$.
