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

arXiv: https://arxiv.org/abs/2010.01845 · HTML: https://mlsanity.com/paper/2010.01845/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Monte Carlo Variational Auto-Encoders](https://mlsanity.com/paper/2106.15921/) (2021)
- [Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transport](https://mlsanity.com/paper/2202.01841/) (2022)
- [eVAE: Evolutionary Variational Autoencoder](https://mlsanity.com/paper/2301.00011/) (2023)
- [Bootstrap Your Flow](https://mlsanity.com/paper/2111.11510/) (2021)
- [NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform](https://mlsanity.com/paper/2103.10943/) (2021)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)
- [Unbiased Derivative Estimation for Stationary Mean of Parameterized Markov chains](https://mlsanity.com/paper/2606.11487/) (2026)

## Abstract (arXiv)

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is challenging since the computation of the marginal likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a ML training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We obtain the estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and with finite variance. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.