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Persistence-based modes inference
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DOI：10.1051/ps/2026003.png)
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Abstract
En 中文
We address the problem of estimating multiple modes of a multivariate density using persistent homology, a central tool in Topological Data Analysis. We introduce a method based on the preliminary estimation of the H0-persistence diagram to infer the number of modes, their locations, and the corresponding local maxima. For broad classes of piecewise-continuous functions with geometric control on discontinuity loci, we identify a critical separation threshold between modes, equiv-alently interpretable in our framework in terms of modes' prominence, below which modes inference is impossible and above which our procedure achieves minimax optimal rates.
Keywords:
Modes inference
non-parametric statistics
topological data analysis
persistent homology
Journal
E
IF:
0.7
Papers:
11
Citations:
0
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