2024/03/28 by Hugo Henneuse, Henneuse, Hugo · 1 citation
Computer Science · Engineering · #Algebraic Topology (math.AT) #FOS: Mathematics #Machine Fault Diagnosis Techniques #Medical Image Segmentation Techniques #Statistics Theory (math.ST) #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.2403.19396
openalex created_date 2024/03/28 · openalex publication_date 2024/03/28 · openalex updated_date 2026/07/28
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 Hölder-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 Hölder-continuous functions.