Variable Selection in Partial Linear Models

Music City Center 

Variable selection in partial linear models (PLMs) is crucial for high-dimensional data analysis, where accurately estimating both linear and nonlinear components is essential. In this work, we develop a methodology based on Variational Bayes (VB) approach for variable selection in PLMs, incorporating a spike-and-slab prior on both the linear coefficients and the parameters of a neural network (NN) that is used to estimate the nonlinear component. The spike-and-slab prior promotes sparsity in the linear component while simultaneously regularizing the neural network, which ensures flexibility in capturing complex nonlinear relationships without overfitting. The VB framework provides an efficient and scalable inference procedure. We evaluate our method against existing approaches by assessing variable selection accuracy for both linear and nonlinear variables. We further check the performance of our method through extensive simulations involving covariates with correlated structure and real-data experiments, where our method demonstrates superior performance, achieving more precise non
linear function estimation as well as variable selection and the same for linear covariates.

Partial Linear Models (PLM)

Variational Bayes(VB)

Neural Network(NN)

Spike-and-Slab

Variable Selection 

Section on Statistical Learning and Data Science