# Prediction-Centric Uncertainty Quantification via MMD

arXiv: https://arxiv.org/abs/2410.11637 · HTML: https://mlsanity.com/paper/2410.11637/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2024.

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

- [TabMGP: Martingale Posterior with TabPFN](https://mlsanity.com/paper/2510.25154/) (2025)
- [Predictive variational inference: Learn the predictively optimal posterior distribution](https://mlsanity.com/paper/2410.14843/) (2024)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields](https://mlsanity.com/paper/2509.26005/) (2025)
- [Robust Bayesian Optimisation with Unbounded Corruptions](https://mlsanity.com/paper/2511.15315/) (2025)
- [Thinned Mean Field Langevin Dynamics](https://mlsanity.com/paper/2605.28589/) (2026)
- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)
- [Priors learned from legacy reconstructions inherit undetectable overconfidence](https://mlsanity.com/paper/2607.21721/) (2026)

## Abstract (arXiv)

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised Bayesian methodologies have been proposed for inference with misspecified models, but these are typically associated with vanishing parameter uncertainty as more data are observed. In the context of a misspecified deterministic mathematical model, this has the undesirable consequence that posterior predictions become deterministic and certain, while being incorrect. Taking this observation as a starting point, we propose Prediction-Centric Uncertainty Quantification, where a mixture distribution based on the deterministic model confers improved uncertainty quantification in the predictive context. Computation of the mixing distribution is cast as a (regularised) gradient flow of the maximum mean discrepancy (MMD), enabling consistent numerical approximations to be obtained. Results are reported on both a toy model from population ecology and a real model of protein signalling in cell biology.