# Sharp Convergence Rates for Forward Regression in High-Dimensional Sparse Linear Models

## TL;DR

This paper provides sharp probabilistic bounds on the prediction error and number of covariates selected by forward regression in high-dimensional sparse linear models, without relying on beta-min or irrepresentability conditions.

## Contribution

It offers the first sharp convergence rate analysis for forward regression in high-dimensional sparse linear models without beta-min or irrepresentability assumptions.

## Key findings

- Probabilistic bounds for prediction error norm
- Bounds on the number of selected covariates
- Analysis applicable to high-dimensional settings

## Abstract

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.