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

06/28/2021 ∙ by Minh-Lien Jeanne Nguyen, et al. ∙ 0

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).

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 9

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.