Affine independent variational inference

We consider inference in a broad class of non-conjugate probabilistic models based on minimising the Kullback-Leibler divergence between the given target density and an approximating ‘variational ’ density. In particular, for generalised linear models we describe approximating densities formed from an affine trans-formation of independently distributed latent variables, this class including many well known densities as special cases. We show how all relevant quantities can be efficiently computed using the fast Fourier transform. This extends the known class of tractable variational approximations and enables the fitting for example of skew variational densities to the target density.