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Rapport (Rapport De Recherche) Année : 2019

Adaptive greedy algorithm for moderately large dimensions in kernel conditional density estimation

Résumé

This paper studies the estimation of the conditional density f (x, ·) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) ∈ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with typically r d. We provide an adaptive fully-nonparametric strategy based on kernel rules to estimate f. To select the bandwidth of our kernel rule, we propose a new fast iterative algorithm inspired by the Rodeo algorithm (Wasserman and Lafferty (2006)) to detect the sparsity structure of f. More precisely, in the minimax setting, our pointwise estimator, which is adaptive to both the regularity and the sparsity, achieves the quasi-optimal rate of convergence. Its computational complexity is only O(dn log n).
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Dates et versions

hal-02085677 , version 1 (31-03-2019)
hal-02085677 , version 2 (28-06-2021)
hal-02085677 , version 3 (22-10-2022)

Identifiants

  • HAL Id : hal-02085677 , version 1

Citer

Minh-Lien Jeanne Nguyen, Claire Lacour, Vincent Rivoirard. Adaptive greedy algorithm for moderately large dimensions in kernel conditional density estimation. [Research Report] Paris Saclay; Paris Est; Paris IX Dauphine. 2019. ⟨hal-02085677v1⟩

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