  Many modern datasets don't fit neatly into $n \times p$ matrices, but most
techniques for measuring statistical stability expect rectangular data. We
study methods for stability assessment on non-rectangular data, using
statistical learning algorithms to extract rectangular latent features. We
design controlled simulations to characterize the power and practicality of
competing approaches. This motivates new strategies for visualizing feature
stability. Our stability curves supplement the direct analysis, providing
information about the reliability of inferences based on learned features.
Finally, we illustrate our approach using a spatial proteomics dataset, where
machine learning tools can augment the scientist's workflow, but where
guarantees of statistical reproducibility are still central. Our raw data,
packaged code, and experimental outputs are publicly available.
