# Hamiltonian Variational Auto-Encoder

arXiv: https://arxiv.org/abs/1805.11328 · HTML: https://mlsanity.com/paper/1805.11328/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

## Built on by (most cited first, 30 of 41)

- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Deep Learning Approaches for Data Augmentation in Medical Imaging: A Review](https://mlsanity.com/paper/2307.13125/) (2023)
- [MCMC Variational Inference via Uncorrected Hamiltonian Annealing](https://mlsanity.com/paper/2107.04150/) (2021)
- [Monte Carlo Variational Auto-Encoders](https://mlsanity.com/paper/2106.15921/) (2021)
- [Differentiable Annealed Importance Sampling and the Perils of Gradient Noise](https://mlsanity.com/paper/2107.10211/) (2021)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Case](https://mlsanity.com/paper/2206.08309/) (2022)
- [Langevin Diffusion Variational Inference](https://mlsanity.com/paper/2208.07743/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey](https://mlsanity.com/paper/2101.00734/) (2021)
- [Improving Lossless Compression Rates via Monte Carlo Bits-Back Coding](https://mlsanity.com/paper/2102.11086/) (2021)
- [Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2202.04599/) (2022)
- [Auto-Encoding Score Distribution Regression for Action Quality Assessment](https://mlsanity.com/paper/2111.11029/) (2021)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Surrogate Likelihoods for Variational Annealed Importance Sampling](https://mlsanity.com/paper/2112.12194/) (2021)
- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [MixFlows: principled variational inference via mixed flows](https://mlsanity.com/paper/2205.07475/) (2022)
- [Alleviating Adversarial Attacks on Variational Autoencoders with MCMC](https://mlsanity.com/paper/2203.09940/) (2022)
- [Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling](https://mlsanity.com/paper/2111.02434/) (2021)
- [Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transport](https://mlsanity.com/paper/2202.01841/) (2022)
- [Learning Proposals for Probabilistic Programs with Inference Combinators](https://mlsanity.com/paper/2103.00668/) (2021)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [Zero-shot-Learning Cross-Modality Data Translation Through Mutual Information Guided Stochastic Diffusion](https://mlsanity.com/paper/2301.13743/) (2023)
- [Embracing the chaos: analysis and diagnosis of numerical instability in variational flows](https://mlsanity.com/paper/2307.06957/) (2023)
- [One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Models](https://mlsanity.com/paper/2305.18900/) (2023)
- [Adaptive Machine Learning for Time-Varying Systems: Low Dimensional Latent Space Tuning](https://mlsanity.com/paper/2107.06207/) (2021)
- [Discriminative Hamiltonian Variational Autoencoder for Accurate Tumor Segmentation in Data-Scarce Regimes](https://mlsanity.com/paper/2406.11659/) (2024)
- [Improving Actor-Critic Reinforcement Learning via Hamiltonian Monte Carlo Method](https://mlsanity.com/paper/2103.12020/) (2021)
- [Multimodal hierarchical Variational AutoEncoders with Factor Analysis latent space](https://mlsanity.com/paper/2207.09185/) (2022)
- [Reparameterized Variational Rejection Sampling](https://mlsanity.com/paper/2309.14612/) (2023)

## Abstract (arXiv)

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.