# Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion prior

arXiv: https://arxiv.org/abs/2310.00097 · HTML: https://mlsanity.com/paper/2310.00097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 29 Sep 2023.

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

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [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)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Concentration of tempered posteriors and of their variational approximations](https://mlsanity.com/paper/1706.09293/) (2017)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Frequentist Consistency of Variational Bayes](https://mlsanity.com/paper/1705.03439/) (2017)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [Convergence Rates of Variational Posterior Distributions](https://mlsanity.com/paper/1712.02519/) (2017)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [On Statistical Optimality of Variational Bayes](https://mlsanity.com/paper/1712.08983/) (2017)
- [Improved Convergence Rates for Sparse Approximation Methods in Kernel-Based Learning](https://mlsanity.com/paper/2202.04005/) (2022)
- [Frequentist coverage and sup-norm convergence rate in Gaussian process regression](https://mlsanity.com/paper/1708.04753/) (2017)
- [Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2106.01121/) (2021)
- [Spike and slab variational Bayes for high dimensional logistic regression](https://mlsanity.com/paper/2010.11665/) (2020)

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

- [Variational Gaussian Processes For Linear Inverse Problems](https://mlsanity.com/paper/2311.00663/) (2023)

## Abstract (arXiv)

We study pointwise estimation and uncertainty quantification for a sparse variational Gaussian process method with eigenvector inducing variables. For a rescaled Brownian motion prior, we derive theoretical guarantees and limitations for the frequentist size and coverage of pointwise credible sets. For sufficiently many inducing variables, we precisely characterize the asymptotic frequentist coverage, deducing when credible sets from this variational method are conservative and when overconfident/misleading. We numerically illustrate the applicability of our results and discuss connections with other common Gaussian process priors.