# Invariant Priors for Bayesian Quadrature

arXiv: https://arxiv.org/abs/2112.01578 · HTML: https://mlsanity.com/paper/2112.01578/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Probabilistic Numerics and Uncertainty in Computations](https://mlsanity.com/paper/1506.01326/) (2015)
- [Bayesian Probabilistic Numerical Methods](https://mlsanity.com/paper/1702.03673/) (2017)
- [Learning Invariances using the Marginal Likelihood](https://mlsanity.com/paper/1808.05563/) (2018)
- [Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature](https://mlsanity.com/paper/1411.0439/) (2014)
- [Emulation of physical processes with Emukit](https://mlsanity.com/paper/2110.13293/) (2021)
- [Convergence Guarantees for Adaptive Bayesian Quadrature Methods](https://mlsanity.com/paper/1905.10271/) (2019)
- [Active Multi-Information Source Bayesian Quadrature](https://mlsanity.com/paper/1903.11331/) (2019)
- [Bayesian Quadrature for Multiple Related Integrals](https://mlsanity.com/paper/1801.04153/) (2018)
- [Improving Quadrature for Constrained Integrands](https://mlsanity.com/paper/1802.04782/) (2018)

## Built on by (most cited first, 2 of 2)

- [Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization](https://mlsanity.com/paper/2401.05716/) (2024)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)

## Abstract (arXiv)

Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode invariance of the integrand under a set of bijective transformations in the input domain, in particular some unitary transformations, such as rotations, axis-flips, or point symmetries. We show initial results on superior performance in comparison to standard Bayesian quadrature on several synthetic and one real world application.