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Activity Number: 416 - SLDS CSpeed 7
Type: Contributed
Date/Time: Thursday, August 12, 2021 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #317976
Title: DebiNet: Debiasing Linear Models with Nonlinear Overparameterized Neural Networks
Author(s): Shiyun Xu* and Zhiqi Bu
Companies: University of Pennsylvania and University of Pennsylvania
Keywords: feature selection; Lasso; neural network; post-selection inference; partially linear model; semiparametric model
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.


Authors who are presenting talks have a * after their name.

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