Density estimation is one of the most classical problem in nonparametric statistics: given i.i.d. samples $X_1, \ldots, X_n$ from a distribution $\mu$ with density $f$ on $R^D$, the goal is to reconstruct the underlying density (say for instance for the $L_p$ norm). This problem is known to become untractable in high dimension $D \gg 1$. We propose to overcome this issue by assuming that the distribution $\mu$ is actually supported around a low dimensional unknown shape $M$, of dimension $d \ll D$. After showing that this problem is degenerate for a large class of standard losses ($L_p$, total variation, etc.), we focus on the Wasserstein loss, for which we build a minimax estimator, based on kernel density estimation, whose rate of convergence depends on d, and on the regularity of the underlying density, but not on the ambient dimension $D$.
Mathieu Ribatet vous invite à une réunion Zoom planifiée.
Sujet : Séminaire MathAppli - Vincent Divol - Density estimation on manifolds: an optimal transport approach
Heure : 8 déc. 2020 11:00 AM Paris
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https://ec-nantes.zoom.us/j/95241226370
ID de réunion : 952 4122 6370
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