# Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes

arXiv: https://arxiv.org/abs/2302.04534 · HTML: https://mlsanity.com/paper/2302.04534/

## Key facts

- Cited by 9 papers in the map (data through 7 Oct 2026).
- Builds on 42 of its 75 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [All You Need is a Good Functional Prior for Bayesian Deep Learning](https://mlsanity.com/paper/2011.12829/) (2020)
- [Resampled Priors for Variational Autoencoders](https://mlsanity.com/paper/1810.11428/) (2018)
- [Bayesian Dark Knowledge](https://mlsanity.com/paper/1506.04416/) (2015)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [Bayesian Variational Autoencoders for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/1912.05651/) (2019)
- [Adversarial Distillation of Bayesian Neural Network Posteriors](https://mlsanity.com/paper/1806.10317/) (2018)
- [Learning to Draw Samples with Amortized Stein Variational Gradient Descent](https://mlsanity.com/paper/1707.06626/) (2017)
- [Longitudinal Variational Autoencoder](https://mlsanity.com/paper/2006.09763/) (2020)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)

## Built on by (most cited first, 9 of 9)

- [Generative Uncertainty in Diffusion Models](https://mlsanity.com/paper/2502.20946/) (2025)
- [One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Models](https://mlsanity.com/paper/2305.18900/) (2023)
- [PPG-to-ECG Signal Translation for Continuous Atrial Fibrillation Detection via Attention-based Deep State-Space Modeling](https://mlsanity.com/paper/2309.15375/) (2023)
- [Preventing Model Collapse in Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2404.01697/) (2024)
- [Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modelling](https://mlsanity.com/paper/2505.16481/) (2025)
- [Deep Latent Variable Modeling of Physiological Signals](https://mlsanity.com/paper/2405.19277/) (2024)
- [PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2505.19320/) (2025)
- [Parameter Space Analysis through Guided Visual Interpolations](https://mlsanity.com/paper/2509.19202/) (2025)
- [Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transport](https://mlsanity.com/paper/2605.20989/) (2026)

## Abstract (arXiv)

Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach qualitatively and quantitatively on a wide range of representation learning and generative modeling tasks and show that our approach consistently outperforms multiple alternatives relying on Variational Autoencoders.