# Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models

arXiv: https://arxiv.org/abs/2610.03647 · HTML: https://mlsanity.com/paper/2610.03647/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 18 of 18)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Structured Stochastic Variational Inference](https://mlsanity.com/paper/1404.4114/) (2014)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [Deep Gaussian Processes with Importance-Weighted Variational Inference](https://mlsanity.com/paper/1905.05435/) (2019)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds](https://mlsanity.com/paper/2210.01672/) (2022)
- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [Latent variable modeling with random features](https://mlsanity.com/paper/2006.11145/) (2020)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [Riemann2: Learning Riemannian Submanifolds from Riemannian Data](https://mlsanity.com/paper/2503.05540/) (2025)
- [Generalised Gaussian Process Latent Variable Models (GPLVM) with Stochastic Variational Inference](https://mlsanity.com/paper/2202.12979/) (2022)
- [Preventing Model Collapse in Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2404.01697/) (2024)
- [Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling](https://mlsanity.com/paper/2408.06710/) (2024)
- [Weighted-Sum of Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2402.09122/) (2024)
- [Multi-View Oriented GPLVM: Expressiveness and Efficiency](https://mlsanity.com/paper/2502.08253/) (2025)

## Abstract (arXiv)

Many machine learning methods aim to approximate the lower-dimensional manifold on which the data lives. A desirable feature of such methods is that they should capture the epistemic uncertainty of this learned manifold. One model that achieves this is the Gaussian Process Latent Variable Model, in which a Gaussian Process (GP) mapping from the latent space provides an estimate of the uncertainty of the manifold. However, the effectiveness of this uncertainty estimation is limited by the mean-field variational approximation between the GP inducing points and the latent variables. In this work, we apply Amortized Structured Stochastic Variational Inference to allow the variational posterior for the latent space to be conditionally dependent on the value of the inducing points. We demonstrate that this more flexible variational posterior improves several metrics relating to the reconstruction of points on the data manifold.