Our paper, "Interpretable Stein Goodness-of-fit Tests on Riemannian Manifold," was published at ICML 2021 (the 38th International Conference on Machine Learning). It's co-authored by Sentinel Assurance co-founder Wenkai Xu, together with Takeru Matsuda (University of Tokyo & RIKEN Center for Brain Science).
What the paper does
- Extends kernel Stein discrepancy theory to build goodness-of-fit tests for distributions defined on Riemannian manifolds, such as tori and rotation groups, instead of assuming flat Euclidean data.
- Works even when the reference model's normalizing constant is unknown or intractable to compute, the common case for realistic models on these spaces.
- Produces an interpretable diagnostic rather than a bare pass/fail statistic: it can point to where and how a model's fit breaks down.
- Backed by asymptotic efficiency analysis and validated on simulations and real datasets.
Our take
A model is only as trustworthy as the tests you can run against it, and most standard testing tools quietly assume the data lives in flat space. A lot of real-world data doesn't. Building tests that work on the actual geometry of the data, and that explain their verdict instead of just returning a number, is the same discipline worth bringing to verifying more complex systems: don't just say something's wrong, show where.