Black Box Variational Inference

TL;DR

Black Box Variational Inference offers a flexible, model-agnostic approach to approximate complex posteriors efficiently using stochastic optimization, enabling rapid model development and evaluation without extensive derivation.

Contribution

The paper introduces a general black box variational inference algorithm that simplifies applying variational methods to diverse models without model-specific derivations.

Findings

Faster convergence to better predictive likelihoods than sampling methods

Effective variance reduction techniques for stochastic gradients

Facilitates rapid exploration of multiple models in healthcare data

Abstract

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data.