Fast Second-Order Stochastic Backpropagation for Variational Inference
This is an incremental improvement for machine learning practitioners using variational inference, offering faster convergence in scalable, model-free settings.
The paper tackles the problem of slow convergence in variational inference by proposing a second-order optimization method based on stochastic backpropagation, which generalizes gradient computation with lower complexity. It demonstrates substantial enhancement in convergence rates on real-world datasets like Bayesian logistic regression and VAEs, compared to other stochastic gradient methods.
We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by generalizing the gradient computation in stochastic backpropagation via a reparametrization trick with lower complexity. As an illustrative example, we apply this approach to the problems of Bayesian logistic regression and variational auto-encoder (VAE). Additionally, we compute bounds on the estimator variance of intractable expectations for the family of Lipschitz continuous function. Our method is practical, scalable and model free. We demonstrate our method on several real-world datasets and provide comparisons with other stochastic gradient methods to show substantial enhancement in convergence rates.