I’d like the parameters φ of my guide q(z|φ) to correspond to ẑ, an SVI estimate of the MAP of z. The guide would thus be a multivariate normal 𝒩(ẑ,ℐ ⁻¹(ẑ)), where the variance ℐ ⁻¹(ẑ) is the inverse of the observed information of z at ẑ; that is, the inverse of the Hessian of the posterior density.
Thus, in order to construct the guide, I need to be able to evaluate the posterior density of the model, and to get the Hessian of that posterior density. I’d like to do that Hessian for a subset of variables at a time, so that I can use what I know about conditional independence to deal with this high-dimensional matrix one low-dimensional part at a time.
Reading the documents, it’s clear to me how to run inference, but when I do so, all the evaluations of the density of the model are inside a black box. Can anybody tell me how I’d evaluate the density of a model m, and how I’d get the Hessian of that density?