Tutorial on Geometric Probabilistic Models

ProbAI 2025

Slides

You can find the slides here.

Note (13.10.2025): RMSE values for graph convolutional neural networks (GCNs) in the slides are incorrect due to a bug in the GCNModel class in the pems-regression package (details here). The only qualitative change is that a deeper GCN performs worse than a shallow one (not better as stated in the slides). All other conclusions remain the same. Corrected RMSE values can be found in this notebook.

Practice

Notebook #1 [Google Colab] can be found here.
You can show/hide solution by clicking here.

Notebook #2 [Google Colab] can be found here.
You can show/hide solution by clicking here.

Extended Notebooks

Euclidean probabilistic models is an extension of Notebook #1 which features Bayesian neural networks and Gaussian process models shown in the slides but not considered in Notebook #1 itself.
It can be found here.

Geometric probabilistic models is an extension of Notebook #2 which features Bayesian graph CNNs and graph Gaussian processes shown in the slides but not considered in Notebook #2 itself.
It can be found here. [Corrected on 13.10.2025, see note above]
Note: with default Google Colab GPUs, this notebook may take a long time (hours) to run.

Materials

Resources on geometric deep learning (including the proto-book): https://geometricdeeplearning.com.
Also, A Gentle Introduction to Graph Neural Networks.

A simple benchmark suite for geometric probabilistic models: https://github.com/vabor112/pems-regression.

Analogs of RBF (and Matérn) kernels on various geometric spaces: https://geometric-kernels.github.io/.

References: as part of the slides.