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Multivariate Gaussian Variational Inference by Natural Gradient Descent

2020-10-19 13:54:16
Timothy D. Barfoot
arXiv_RO
           
Abstract

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.

Abstract (translated)

URL

https://arxiv.org/abs/2001.10025

PDF

https://arxiv.org/pdf/2001.10025.pdf

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