# Probability-Generating Function Kernels for Spherical Data

arXiv: https://arxiv.org/abs/2112.00365 · HTML: https://mlsanity.com/paper/2112.00365/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity](https://mlsanity.com/paper/1602.05897/) (2016)
- [Dirichlet-based Gaussian Processes for Large-scale Calibrated Classification](https://mlsanity.com/paper/1805.10915/) (2018)
- [Octree guided CNN with Spherical Kernels for 3D Point Clouds](https://mlsanity.com/paper/1903.00343/) (2019)
- [Exact heat kernel on a hypersphere and its applications in kernel SVM](https://mlsanity.com/paper/1702.01373/) (2017)
- [Mehler's Formula, Branching Process, and Compositional Kernels of Deep Neural Networks](https://mlsanity.com/paper/2004.04767/) (2020)

## Abstract (arXiv)

Probability-generating function (PGF) kernels are introduced, which constitute a class of kernels supported on the unit hypersphere, for the purposes of spherical data analysis. PGF kernels generalize RBF kernels in the context of spherical data. The properties of PGF kernels are studied. A semi-parametric learning algorithm is introduced to enable the use of PGF kernels with spherical data.