Persistence Diagram Estimation of Multivariate Piecewise H\"older-continuous Signals

Hugo Henneuse

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arXiv · 2403.19396

Persistence Diagram Estimation of Multivariate Piecewise H\"older-continuous Signals

Hugo Henneuse

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Abstract

To our knowledge, the analysis of convergence rates for persistence diagrams estimation from noisy signals has predominantly relied on lifting signal estimation results through sup-norm (or other functional norm) stability theorems. We believe that moving forward from this approach can lead to considerable gains. We illustrate it in the setting of nonparametric regression. From a minimax perspective, we examine the inference of persistence diagrams (for the sublevel sets filtration). We show that for piecewise H\"older-continuous functions, with control over the reach of the set of discontinuities, taking the persistence diagram coming from a simple histogram estimator of the signal permits achieving the minimax rates known for H\"older-continuous functions.

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Hugo Henneuse. 2024-03-28. Persistence Diagram Estimation of Multivariate Piecewise H\"older-continuous Signals. https://arxiv.org/abs/2403.19396

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