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Pré-Publication, Document De Travail Année : 2020

Statistical Query Complexity of Manifold Estimation

Eddie Aamari
Alexander Knop
  • Fonction : Auteur

Résumé

This paper studies the statistical query (SQ) complexity of estimating $d$-dimensional submanifolds in $\mathbb{R}^n$. We propose a purely geometric algorithm called Manifold Propagation, that reduces the problem to three natural geometric routines: projection, tangent space estimation, and point detection. We then provide constructions of these geometric routines in the SQ framework. Given an adversarial $\mathrm{STAT}(\tau)$ oracle and a target Hausdorff distance precision $\varepsilon = \Omega(\tau^{2 / (d + 1)})$, the resulting SQ manifold reconstruction algorithm has query complexity $O(n \operatorname{polylog}(n) \varepsilon^{-d / 2})$, which is proved to be nearly optimal. In the process, we establish low-rank matrix completion results for SQ's and lower bounds for randomized SQ estimators in general metric spaces.
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Dates et versions

hal-02995288 , version 1 (09-11-2020)
hal-02995288 , version 2 (12-10-2022)

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  • HAL Id : hal-02995288 , version 1

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Eddie Aamari, Alexander Knop. Statistical Query Complexity of Manifold Estimation. 2020. ⟨hal-02995288v1⟩
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