BBVI

A collection of Black Box Variational Inference algorithms implemented in an object-oriented Python framework using Autograd.

bbvi.py provides a class BaseBBVIModel which is a base class for a general Bayesian inference problem to be solved by variational methods. Specifically, if we have a posterior p(z|x), BaseBBVIModel provides the framework and machinery to approximate p(z|x) by a distribution q(z|lambda) where lambda is the variational parameter(s) that determines the variational family. This is based on some excellent models found at https://github.com/HIPS/autograd/blob/master/examples/.

How to use

1. Derive a model class from BaseBBVIModel which requires that you implement the log-posterior, the log-variational approximation, a sampler of the variational approximation, and a parameter-handler.
2. Chose an ELBO gradient estimator (more on this below).
3. Call the method run_VI with the appropriate initial parameters.

Available ELBO Estimators

This framework is designed to facilitate rapid experimentation with different BBVI methods. We have provided three ELBO gradient estimators, but it is a simple matter to add others afterward. The estimators broadly fall into two categories: "stochastic search" and "reparameterization":

Stochastic Search

These follow the original approach of Ranganath et al. (https://arxiv.org/abs/1401.0118) and uses the gradient of the variational distribution.

• how='stochsearch': The original method from Ranganath et al. (2013) (https://arxiv.org/abs/1401.0118).

Reparameterization

These follow the approach taken in Kingma et al. (https://arxiv.org/abs/1506.02557) by parameterizing the samples then using backprop.

• how='reparam': The original method from Kingma et al. (2015) (https://arxiv.org/abs/1506.02557) and following the implementation from http://www.cs.toronto.edu/~duvenaud/papers/blackbox.pdf.
• how='noscore': A clever and simple variant of reparameterization that omits the score function from the derivative estimate from Roder et al. (2017) https://papers.nips.cc/paper/7268-sticking-the-landing-simple-lower-variance-gradient-estimators-for-variational-inference.pdf

We should also note that various enhancements to these models (Rao-Blackwellization, control variates) were considered but omitted because neither is easily applied to a black-box model. These models could be specialized to include these enhancements on a case-by-case basis.

Examples

Three examples are provided, BBVI_test1.py and BBVI_test2.py deal with using a mutlivariate Gaussian to approximate a highly non-normal distribution. BBVI_test3.py shows how to do inference on the weights of a MLP. It is worthwhile noting that the variational approximation and much of the code is essentially the same in each example, and only the details of the specific problem need to be adjusted.