Estimation non paramétrique de densités conditionnelles : grande dimension, parcimonie et algorithmes gloutons.

Abstract : We consider the problem of conditional density estimation in moderately large dimen- sions. Much more informative than regression functions, conditional densities are of main interest in recent methods, particularly in the Bayesian framework (studying the posterior distribution, find- ing its modes...). After recalling the estimation issues in high dimension in the introduction, the two following chapters develop on two methods which address the issues of the curse of dimensionality: being computationally efficient by a greedy iterative procedure, detecting under some suitably defined sparsity conditions the relevant variables, while converging at a quasi-optimal minimax rate. More precisely, the two methods consider kernel estimators well-adapted for conditional density estimation and select a pointwise multivariate bandwidth by revisiting the greedy algorithm RODEO (Regular- isation Of Derivative Expectation Operator). The first method having some initialization problems and extra logarithmic factors in its convergence rate, the second method solves these problems, while adding adaptation to the smoothness. In the penultimate chapter, we discuss the calibration and nu- merical performance of these two procedures, before giving some comments and perspectives in the last chapter.
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Minh-Lien Jeanne Nguyen. Estimation non paramétrique de densités conditionnelles : grande dimension, parcimonie et algorithmes gloutons.. Statistiques [math.ST]. Université Paris-Saclay, 2019. Français. ⟨NNT : 2019SACLS185⟩. ⟨tel-02289115⟩

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