variational inference with normalizing flows

10 January 2017

notes on (Rezende & Mohamed, 2015).

summary

couldn’t find code… closest things was https://github.com/casperkaae/parmesan/issues/22

setup: probabilistic model $p_{\theta}(z, x) = p_{\theta}(z) p_{\theta}(x \given z)$ of latents $z$, observes $x$, parametrized by model parameters $\theta$. interested in $p_{\theta}(z \given x)$.

the main problem addressed by this paper is choosing the family of variational approximations $\mathcal Q$ so that the true posterior $p_{\theta}(z \given x) \in \mathcal Q$. the usual way of doing this is to fix a parametrized family $\mathcal Q = \{q_{\phi}: \phi \in \Phi\}$, most commonly mean-field. the authors argue that this hardly covers the true posterior.

instead, $\mathcal Q$ is induced by successive transformations $f_1, \dotsc, f_K$ on a sample $z_0$ from some initial distribution $q_0(z_0)$. the density of the $q$s thus has jacobian terms (which must be cheap to evaluate). they derive the ELBO in this setting (eqn 15).

references

1. Rezende, D., & Mohamed, S. (2015). Variational Inference with Normalizing Flows. In Proceedings of the 32nd International Conference on Machine Learning (ICML-15) (pp. 1530–1538).
@inproceedings{rezende2015variational,
title = {Variational Inference with Normalizing Flows},
author = {Rezende, Danilo and Mohamed, Shakir},
booktitle = {Proceedings of the 32nd International Conference on Machine Learning (ICML-15)},
pages = {1530--1538},
year = {2015},