Rodeo: Sparse, greedy nonparametric regression

Rodeo: Sparse Nonparametric Regression in High Dimensions

We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large. The method--called rodeo (regularization of derivative expectation operator)--conducts a sequence of hypothesis tests to threshold derivatives, and is easy to implement. Under certain assumptions on the regression function and sampling density, it is shown that t…

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

This paper studies the estimation of the conditional density f (x, $\times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $\in$ 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, whi…

Nonparametric method for space conditional density estimation in moderately large dimensions

In this paper, we consider the problem of estimating a conditional density in moderately large dimensions. Much more informative than regression functions, conditional densities are of main interest in recent methods, particularly in the Bayesian framework (studying the posterior distribution, finding its modes...). Considering a recently studied family of kernel estimators, we select a pointwise multivariate bandwidth by revisiting the greedy algorithm Rodeo (Regularisation Of Derivative Expectation Operator). The method addresses several issues: being greedy and computationally efficient by …

通过异质数据源投注的主动非参数两样本检验

Active Nonparametric Two-Sample Testing by Betting on Heterogeneous Data Sources

本文提出了一种基于投注框架的主动非参数两样本检验方法，通过自适应选择异质数据源以提高检验效率和准确性。

Nonparametric Independence Screening in Sparse Ultra-High Dimensional Varying Coefficient Models

The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection arrives. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in ultra-high dimensional sparse varying-coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sur…

非参数图模型的贪婪等价搜索

Greedy equivalence search for nonparametric graphical models

针对一般非参数 DAG 模型缺乏一致性理论的问题，本文利用非参数贝叶斯进展构建模型检验方法，证明了贪婪等价搜索（GES）在满足马尔可夫分解平滑条件的一般 DAG 模型族上的一致性。