Hamiltonian Variational Auto-Encoder

By Anthony L. Caterini, Arnaud Doucet, Dino Sejdinovic. 2018

103 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Sergey Levine
2. Bo Dai
3. Le Song
4. Qiang Liu
5. George Tucker
6. Arthur Gretton
7. Yoshua Bengio
8. Stefano Ermon

In Computer Vision and Pattern Recognition

1. Arash Vahdat
2. Luc Van Gool
3. Le Song
4. Bo Dai
5. Dacheng Tao
6. Xiaogang Wang
7. Ming-Hsuan Yang
8. Trevor Darrell

In Statistical and Nonlinear Physics

1. Arash Vahdat
2. Evgeny Andriyash
3. Arthur Gretton
4. William G. Macready
5. Matthew D. Hoffman
6. Rajesh Ranganath
7. Hanjun Dai
8. Dustin Tran

In Probabilistic & Bayesian Methods

1. Arthur Gretton
2. Dustin Tran
3. Rajesh Ranganath
4. David M. Blei
5. Bo Dai
6. Bernhard Schölkopf
7. Le Song
8. Matthew D. Hoffman

Citations in the corpus

• Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, background): “Hamiltonian Monte Carlo [54] is another choice which can also be embedded in this framework as done by [61, 10].”
• NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport (2019, background): “Several (e.g.; Salimans et al., 2015; Zhang et al., 2018; Caterini et al., 2018) have considered usingMCMC-based variational bounds to do approximate maximum-likelihood training of variational autoencoders (VAEs).”
• Undirected Graphical Models as Approximate Posteriors (2019, methodology): “Variational Inference and MCMC: A common alternative to variational inference is to use MCMC to sample directly from true posteriors in generative models (Welling & Teh, 2011; Salimans et al., 2015; Wolf et al., 2016; Hoffman, 2017; Li et al., 2017; Caterini et al., 2018).”
• Exponential Family Estimation via Adversarial Dynamics Embedding (2019, methodology): “We start with the embedding of classical Hamiltonian dynamics (Neal, 2011; Caterini et al., 2018) for the dual sampler parametrization, as a concrete example, then discuss its generalization in latent space and the stochastic Langevin dynamics embedding.”