DebiNet: Debiasing Linear Models with Nonlinear Overparameterized Neural Networks
This work addresses the challenge of combining interpretability from linear models with the approximation power of neural networks for researchers and practitioners in high-dimensional statistics, representing an incremental advancement.
The paper tackles the problem of bridging inference and prediction in high-dimensional linear models by incorporating over-parameterized neural networks into semi-parametric models, achieving consistent parameter estimation and improved performance in post-selection inference and generalization error.
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.