Psi-Resilience: Model-Free Feature Importance from 1D Topological Signals

Psi-Resilience is a model-free feature importance method that derives explanations directly from the data itself via 1D topological signals. The method constructs a class-disagreement landscape by estimating class-conditional densities and taking their pointwise absolute difference along the feature axis. Then, the 0-dimensional persistence of this 1D signal defines a resilience functional that aggregates only those topological features that survive perturbations up to a robustness scale which is set by the user. This gives us a context-robust importance score that is inherently auditable via the underlying 1D landscapes and their persistence. The experimental results on both real and synthetic datasets show that Psi-Resilience is a stable explanation method that enables rigorous, distribution-level auditing of feature importance without relying on a predictive model.