Learning variational autoencoders via MCMC speed measures
This work addresses a known bottleneck in deep latent variable models for researchers in generative modeling, but it is incremental as it builds on existing MCMC-based variational methods.
The paper tackles the problem of improving variational autoencoders by using gradient-based MCMC methods to adapt proposal distributions, resulting in higher held-out log-likelihoods and better generative metrics.
Variational autoencoders (VAEs) are popular likelihood-based generative models which can be efficiently trained by maximizing an Evidence Lower Bound (ELBO). There has been much progress in improving the expressiveness of the variational distribution to obtain tighter variational bounds and increased generative performance. Whilst previous work has leveraged Markov chain Monte Carlo (MCMC) methods for the construction of variational densities, gradient-based methods for adapting the proposal distributions for deep latent variable models have received less attention. This work suggests an entropy-based adaptation for a short-run Metropolis-adjusted Langevin (MALA) or Hamiltonian Monte Carlo (HMC) chain while optimising a tighter variational bound to the log-evidence. Experiments show that this approach yields higher held-out log-likelihoods as well as improved generative metrics. Our implicit variational density can adapt to complicated posterior geometries of latent hierarchical representations arising in hierarchical VAEs.