Pretraining and the lasso

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Pre-training is a machine learning technique that leverages knowledge from large datasets to improve model performance on smaller datasets.
• Common applications include fine-tuning deep neural networks for image classification tasks.
• The effectiveness of pre-training for regularization methods like the lasso has not been extensively explored.

Purpose of the Study:

• To investigate the utility of pre-training for the lasso regularization technique.
• To propose a novel framework for lasso pre-training and fine-tuning.
• To explore applications in stratified and multi-response models.

Main Methods:

• A framework is proposed where the lasso model is initially fit on a large dataset (pre-training).
• The pre-trained lasso model is then fine-tuned on a smaller, related dataset.
• The framework is applied to stratified models, estimating common and group-specific coefficients sequentially.

Main Results:

• Lasso pre-training demonstrates superior support recovery for common coefficients in stratified models compared to standard lasso.
• The fine-tuning approach allows for adaptation to smaller or related datasets, including subsets of the original data.
• Separating the estimation of common and individual coefficients enhances scientific interpretability.

Conclusions:

• Pre-training offers a valuable paradigm for enhancing lasso regression, particularly in scenarios with limited data or complex structures.
• The proposed lasso pre-training framework improves coefficient estimation and provides better scientific understanding.
• This approach has broad applicability in statistical modeling, including stratified and multi-response settings.