# Scalable Bayesian inference for heat kernel Gaussian processes on manifolds

arXiv: https://arxiv.org/abs/2405.13342 · HTML: https://mlsanity.com/paper/2405.13342/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2024.

## Built on by (most cited first, 4 of 4)

- [The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphs](https://mlsanity.com/paper/2407.08086/) (2024)
- [Statistical Opportunities in Neuroimaging](https://mlsanity.com/paper/2602.12974/) (2026)
- [Atlas Gaussian processes on restricted domains and point clouds](https://mlsanity.com/paper/2511.15822/) (2025)
- [Sparse Bayesian Modeling of EEG Channel Interactions Improves P300 Brain-Computer Interface Performance](https://mlsanity.com/paper/2602.17772/) (2026)

## Abstract (arXiv)

We establish a scalable manifold learning method and theory, motivated by the problem of estimating fMRI activation manifolds in the Human Connectome Project (HCP). Our primary contribution is the development of an efficient estimation technique for heat kernel Gaussian processes in the exponential family model. This approach handles large sample sizes n, preserves the intrinsic geometry of data, and significantly reduces computational complexity from O(n3) to O(n) via a novel reduced-rank approximation of the graph Laplacian's transition matrix and a Truncated Singular Value Decomposition for the eigenpair computation. The numerical experiments demonstrate the scalability and improved accuracy of our method for manifold learning tasks involving complex large-scale data.