# Accurate and Scalable Stochastic Gaussian Process Regression via Learnable Coreset-based Variational Inference

arXiv: https://arxiv.org/abs/2311.01409 · HTML: https://mlsanity.com/paper/2311.01409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 2 Nov 2023.

## Builds on (most cited first, 7 of 7)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Automated Scalable Bayesian Inference via Hilbert Coresets](https://mlsanity.com/paper/1710.05053/) (2017)
- [Black-box Coreset Variational Inference](https://mlsanity.com/paper/2211.02377/) (2022)

## Built on by (most cited first, 1 of 1)

- [Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices](https://mlsanity.com/paper/2609.30348/) (2026)

## Abstract (arXiv)

We introduce a novel stochastic variational inference method for Gaussian process (GP) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form variational families for stochastic inference, our coreset-based variational GP (CVGP) is defined in terms of the GP prior and the (weighted) data likelihood. This formulation naturally incorporates inductive biases of the prior, and ensures its kernel and likelihood dependencies are shared with the posterior. We derive a variational lower-bound on the log-marginal likelihood by marginalizing over the latent GP coreset variables, and show that CVGP's lower-bound is amenable to stochastic optimization. CVGP reduces the dimensionality of the variational parameter search space to linear O(M) complexity, while ensuring numerical stability at O(M3) time complexity and O(M2) space complexity.