DebiNet: Debiasing Linear Models with Nonlinear Overparameterized Neural Networks

TL;DR

DebiNet integrates over-parameterized neural networks into semi-parametric linear models to improve inference and prediction, enabling debiasing of regularized estimators and combining neural network approximation with linear interpretability.

Contribution

The paper introduces DebiNet, a framework that uses neural networks within semi-parametric models to achieve debiasing and accurate inference in high-dimensional settings.

Findings

DebiNet effectively debiases regularized estimators like Lasso.

The approach combines neural network approximation with linear model interpretability.

Numerical experiments demonstrate improved inference and prediction accuracy.

Abstract

Recent years have witnessed strong empirical performance of over-parameterized neural networks on various tasks and many advances in the theory, e.g. the universal approximation and provable convergence to global minimum. In this paper, we incorporate over-parameterized neural networks into semi-parametric models to bridge the gap between inference and prediction, especially in the high dimensional linear problem. By doing so, we can exploit a wide class of networks to approximate the nuisance functions and to estimate the parameters of interest consistently. Therefore, we may offer the best of two worlds: the universal approximation ability from neural networks and the interpretability from classic ordinary linear model, leading to both valid inference and accurate prediction. We show the theoretical foundations that make this possible and demonstrate with numerical experiments. Furthermore, we propose a framework, DebiNet, in which we plug-in arbitrary feature selection methods to our semi-parametric neural network. DebiNet can debias the regularized estimators (e.g. Lasso) and perform well, in terms of the post-selection inference and the generalization error.