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On the Bootstrap for Persistence Diagrams and Landscapes
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Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confidence bands for persistence landscapes.
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Cited by 2 Pith papers
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From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
STRAND treats persistence diagrams as survival data to derive a calibrated two-sample test, interpretable effect sizes, and a 1-Wasserstein-stable feature vector from one representation.
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Topology of Out-of-Distribution Examples in Deep Neural Networks
Out-of-distribution images show longer average H0 persistence lifetimes in a ResNet18 embedding layer than in-distribution training and test images.
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