Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models
Abstract
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.
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BibTeX
@misc{tretiakov2026amortized,
title = {{Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models}},
author = {Maksym Tretiakov and Sarah Filippi and Vincent Fortuin and Ruth Misener and Ruby Sedgwick and James Odgers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03647},
eprint = {2610.03647},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03647},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models
AU - Maksym Tretiakov
AU - Sarah Filippi
AU - Vincent Fortuin
AU - Ruth Misener
AU - Ruby Sedgwick
AU - James Odgers
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.03647
UR - https://arxiv.org/abs/2610.03647
AB - 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.
ER -