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.