CDRodeo: Adaptive iterative bandwidth selection of kernel rules for multivariate conditional density estimation
Minh-Lien Jeanne NGUYEN

This talk will focus on estimating the conditional density f of a random vector of interest Y given a
vector of auxiliary variables X, given the observation of an i.i.d. sample of the couple (X, Y ).
Our strategy is fully-nonparametric and addresses the case of sparse conditional density in moderately large dimension: more precisely, we assume that f depends only on r unknown components, with typically r<<d. Based on kernel rules, we propose a new fast iterative algorithm inspired by the Rodeo algorithm [3, 2] to select the bandwidth. In the minimax setting where f is s-Hölderian (with s unknown), we prove that our adaptive estimator achieves the quasi-optimal rate of convergence with a competitive computational complexity of O(dn log n) operations.

Keywords: conditional density, high dimension, minimax rates, kernel density estimators, greedy algorithm, sparsity, nonparametric inference.
[1] Nguyen, M.-L.J. (2018, pré-publication) Nonparametric method for sparse conditional density estimation in moderately large dimensions. hal-01688664.
[2] Lafferty J.D., Wasserman L.A. (2008) Rodeo: Sparse, greedy nonparametric regression. Annals of Statistics, Vol. 36, No. 1, 28-63.
[3] Liu H., Lafferty J.D., Wasserman L.A. (2007) Sparse Nonparametric Density Estimation in High
Dimensions Using the Rodeo. AISTATS, 283-290.