Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
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COMPLEX is a closed‑form, training‑free embedding for multiparameter persistence modules that provides both an upper and a lower Lipschitz bound, enabling faithful feature representations. By slicing modules along a near‑diagonal net and embedding each slice with the certified PLACE/PALACE landmark map, the method guarantees that separated modules remain separated in the embedding. On Orbit benchmarks and molecular graph tasks, COMPLEX achieves state‑of‑the‑art accuracy, outperforming existing landmark, transformer, and graph‑based approaches.
SpatialUQ is a post‑hoc uncertainty quantification method that uses only the output probabilities of frozen black‑box vision models. It computes the Jensen‑Shannon divergence between the global prediction and the mean of five fixed spatial crops across six deterministic forward passes, assuming that trustworthy predictions are spatially consistent. On the NIH ChestX‑ray14 dataset, SpatialUQ’s Multicrop Uncertainty Score (MUS) achieves a 0.784 failure‑detection AUC—significantly higher than MC‑Dropout—while also providing superior native calibration and improving further when fused with other uncertainty signals.
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