# Tighter sparse variational Gaussian processes

arXiv: https://arxiv.org/abs/2502.04750 · HTML: https://mlsanity.com/paper/2502.04750/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 8 of 8)

- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [Deep Gaussian Processes for Regression using Approximate Expectation Propagation](https://mlsanity.com/paper/1602.04133/) (2016)
- [Deep convolutional Gaussian processes](https://mlsanity.com/paper/1810.03052/) (2018)
- [Tighter Bounds on the Log Marginal Likelihood of Gaussian Process Regression Using Conjugate Gradients](https://mlsanity.com/paper/2102.08314/) (2021)
- [Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition](https://mlsanity.com/paper/2106.05992/) (2021)

## Built on by (most cited first, 3 of 3)

- [New Bounds for Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2502.08730/) (2025)
- [Sparse Gaussian Processes: Structured Approximations and Power-EP Revisited](https://mlsanity.com/paper/2507.02377/) (2025)
- [Transformed Latent Variable Multi-Output Gaussian Processes](https://mlsanity.com/paper/2605.05133/) (2026)

## Abstract (arXiv)

Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation. This paper introduces a provably tighter variational approximation by relaxing the standard assumption that the conditional approximate posterior given the inducing points must match that in the prior. The key innovation is to modify the conditional posterior to have smaller variances than that of the prior at the training points. We derive the collapsed bound for the regression case, describe how to use the proposed approximation in large data settings, and discuss its application to handle orthogonally structured inducing points and GP latent variable models. Extensive experiments on regression benchmarks, classification, and latent variable models demonstrate that the proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining the same computational cost. An implementation will be made available in all popular GP packages.