Feedback-Controlled Sequential Lasso Screening
This addresses memory constraints in lasso optimization for large-scale data, but it is incremental as it builds on prior sequential screening methods.
The paper tackled the problem of solving lasso problems with large dictionaries that exceed memory limits by proposing a feedback-controlled sequential screening scheme for a fixed regularization parameter, demonstrating it on datasets including one with approximately 100,000 by 300,000 features.
One way to solve lasso problems when the dictionary does not fit into available memory is to first screen the dictionary to remove unneeded features. Prior research has shown that sequential screening methods offer the greatest promise in this endeavor. Most existing work on sequential screening targets the context of tuning parameter selection, where one screens and solves a sequence of $N$ lasso problems with a fixed grid of geometrically spaced regularization parameters. In contrast, we focus on the scenario where a target regularization parameter has already been chosen via cross-validated model selection, and we then need to solve many lasso instances using this fixed value. In this context, we propose and explore a feedback controlled sequential screening scheme. Feedback is used at each iteration to select the next problem to be solved. This allows the sequence of problems to be adapted to the instance presented and the number of intermediate problems to be automatically selected. We demonstrate our feedback scheme using several datasets including a dictionary of approximate size 100,000 by 300,000.