# Reducing Sampling Ratios Improves Bagging in Sparse Regression

## TL;DR

This paper demonstrates that reducing the bootstrap sampling ratio in Bagging enhances sparse regression performance, especially with fewer measurements, outperforming traditional L1 minimization and Bolasso methods.

## Contribution

It introduces a generalized Bagging framework with variable bootstrap ratios for sparse regression and provides theoretical analysis of performance limits.

## Key findings

- Lower bootstrap ratio (60%-90%) improves recovery performance.
- Reduced sampling rate increases SNR by up to 24%.
- A small number of estimates (K=30) suffices for good results.

## Abstract

Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in sparse regression over the baseline method (L1 minimization). The framework employs the generalized version of the original Bagging with various bootstrap ratios. The performance limits associated with different choices of bootstrap sampling ratio L/m and number of estimates K is analyzed theoretically. Simulation shows that the proposed method yields state-of-the-art recovery performance, outperforming L1 minimization and Bolasso in the challenging case of low levels of measurements. A lower L/m ratio (60% - 90%) leads to better performance, especially with a small number of measurements. With the reduced sampling rate, SNR improves over the original Bagging by up to 24%. With a properly chosen sampling ratio, a reasonably small number of estimates K = 30 gives satisfying result, even though increasing K is discovered to always improve or at least maintain the performance.