  This short note reviews so-called Natural Gradient Descent (NGD) for
multivariate Gaussians. The Fisher Information Matrix (FIM) is derived for
several different parameterizations of Gaussians. Careful attention is paid to
the symmetric nature of the covariance matrix when calculating derivatives. We
show that there are some advantages to choosing a parameterization comprising
the mean and inverse covariance matrix and provide a simple NGD update that
accounts for the symmetric (and sparse) nature of the inverse covariance
matrix.
