# Probabilistic selection of inducing points in sparse Gaussian processes

arXiv: https://arxiv.org/abs/2010.09370 · HTML: https://mlsanity.com/paper/2010.09370/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanics](https://mlsanity.com/paper/2409.10972/) (2024)
- [Amortized Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/2409.12301/) (2024)
- [On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach](https://mlsanity.com/paper/2103.03321/) (2021)
- [Inducing Gaussian Process Networks](https://mlsanity.com/paper/2204.09889/) (2022)
- [Review of Recent Advances in Gaussian Process Regression Methods](https://mlsanity.com/paper/2409.08112/) (2024)
- [A Dynamic, Ordinal Gaussian Process Item Response Theoretic Model](https://mlsanity.com/paper/2504.02643/) (2025)
- [Ultra Low-Power, Lightweight, Probabilistic RSS-Based Path Reconstruction: A System for Landscape-Scale Bee Tracking](https://mlsanity.com/paper/2608.27152/) (2026)
- [On Basis Function Selection for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2609.26624/) (2026)

## Abstract (arXiv)

Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing points is generally not associated with uncertainty which prevents us from applying the apparatus of Bayesian reasoning for identifying an appropriate trade-off. In this work we place a point process prior on the inducing points and approximate the associated posterior through stochastic variational inference. By letting the prior encourage a moderate number of inducing points, we enable the model to learn which and how many points to utilise. We experimentally show that fewer inducing points are preferred by the model as the points become less informative, and further demonstrate how the method can be employed in deep Gaussian processes and latent variable modelling.