Conditional nonparametric variable screening by neural factor regression

TL;DR

This paper introduces a neural network-based nonparametric variable screening method that accounts for latent factors, providing a powerful tool for high-dimensional data analysis with proven asymptotic properties.

Contribution

It proposes a novel conditional screening test using neural networks and smoothing techniques to effectively identify additional predictor contributions in high-dimensional, factor-structured data.

Findings

The test achieves asymptotic normality under the null hypothesis.

It is consistent for detecting local alternatives.

Demonstrated effectiveness in simulations and real data applications.

Abstract

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.