DeepAI AI Chat
Log In Sign Up

Hamiltonian Variational Auto-Encoder

by   Anthony L. Caterini, et al.
University of Oxford

Variational Auto-Encoders (VAEs) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (ELBOs). Combined with stochastic variational inference, this provides a methodology scaling to large datasets. However, for this methodology to be practically efficient, it is necessary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the parameters of interest. While the use of Markov chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo (HMC) has been previously suggested to achieve this [23, 26], the proposed methods require specifying reverse kernels which have a large impact on performance. Additionally, the resulting unbiased estimator of the ELBO for most MCMC kernels is typically not amenable to the reparameterization trick. We show here how to optimally select reverse kernels in this setting and, by building upon Hamiltonian Importance Sampling (HIS) [17], we obtain a scheme that provides low-variance unbiased estimators of the ELBO and its gradients using the reparameterization trick. This allows us to develop a Hamiltonian Variational Auto-Encoder (HVAE). This method can be reinterpreted as a target-informed normalizing flow [20] which, within our context, only requires a few evaluations of the gradient of the sampled likelihood and trivial Jacobian calculations at each iteration.


page 1

page 2

page 3

page 4


Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains

The variational auto-encoder (VAE) is a deep latent variable model that ...

Monte Carlo Variational Auto-Encoders

Variational auto-encoders (VAE) are popular deep latent variable models ...

MCMC Variational Inference via Uncorrected Hamiltonian Annealing

Given an unnormalized target distribution we want to obtain approximate ...

Quasi-symplectic Langevin Variational Autoencoder

Variational autoencoder (VAE) as one of the well investigated generative...

Reconsidering Analytical Variational Bounds for Output Layers of Deep Networks

The combination of the re-parameterization trick with the use of variati...

Langevin Autoencoders for Learning Deep Latent Variable Models

Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for...

Posterior Estimation Using Deep Learning: A Simulation Study of Compartmental Modeling in Dynamic PET

Background: In medical imaging, images are usually treated as determinis...