Sharp Convergence Rates for Forward Regression in High-Dimensional Sparse Linear Models
This work addresses model selection and estimation in high-dimensional statistics, providing theoretical guarantees for a widely used method, though it appears incremental as it refines existing analysis.
The paper analyzes forward regression in high-dimensional sparse linear models, proving sharp probabilistic bounds for prediction error and covariate selection without requiring beta-min or irrepresentability conditions.
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters are estimated by least squares. This paper analyzes forward regression in high-dimensional sparse linear models. Probabilistic bounds for prediction error norm and number of selected covariates are proved. The analysis in this paper gives sharp rates and does not require beta-min or irrepresentability conditions.