Conditional nonparametric variable screening by neural factor regression

2024-08-20 · Jianqing Fan, Weining Wang, Yue Zhao

High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors or more generally a set of variables. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and a observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and two real world applications.

📄 PDF Abstract BibTeX arXiv:2408.10825

Code (0)

등록된 구현이 없습니다.

Tasks

regression

Methods 이 논문이 사용한 방법론

SET Dynamic Sparse Training method where weight mask is updated randomly periodically

Convolution A convolution is a type of matrix operation, consisting of a kernel, a small matrix of weights, that slides over input data performing element-wise multiplication with the…

Faithful Variable Screening for High-Dimensional Convex Regression

2014-11-07 · Min Xu, Minhua Chen, John Lafferty

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables…

Additive models regression Variable Selection Vocal Bursts Intensity Prediction

Deep Bootstrap

2026-02-11 · Jinyuan Chang, Yuling Jiao, Lican Kang, Junjie Shi arxiv

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the resp…

Nonparametric Estimation of Truncated Conditional Expectation Functions

2021-09-13 · Tomasz Olma

Truncated conditional expectation functions are objects of interest in a wide range of economic applications, including income inequality measurement, financial risk management, and impact evaluation. They typically invo…

Management regression

Nonparametric Independence Screening via Favored Smoothing Bandwidth

2017-11-28 · Yang Feng, Yi-Chao Wu, Leonard Stefanski

We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression…

Model Selection regression

Conformal Prediction for Nonparametric Instrumental Regression

2026-03-26 · Masahiro Kato arxiv

We propose a method for constructing distribution-free prediction intervals in nonparametric instrumental variable regression (NPIV), with finite-sample coverage guarantees. Building on the conditional guarantee framewor…