Fast Approximate Determinants Using Rational Functions
Abstract
We show how rational function approximations to the logarithm, such as
$\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$,
can be turned into fast algorithms for approximating the determinant
of a very large matrix. We empirically demonstrate that these
algorithms are
under some circumstances better than existing state-of-the-art determinant
approximations for the matrices coming from several popular Gaussian
process kernels, including Matérn-$5/2$ and radial basis functions.
$\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$,
can be turned into fast algorithms for approximating the determinant
of a very large matrix. We empirically demonstrate that these
algorithms are
under some circumstances better than existing state-of-the-art determinant
approximations for the matrices coming from several popular Gaussian
process kernels, including Matérn-$5/2$ and radial basis functions.
