Training Data Subset Selection for Regression with Controlled Generalization Error

TL;DR

This paper introduces SELCON, an efficient algorithm for selecting training data subsets in L2 regularized regression, balancing training speed and accuracy with theoretical guarantees and improved empirical performance.

Contribution

The paper formulates a novel subset selection problem with validation error bounds, proves properties of the objective function, and develops SELCON, an approximation algorithm with theoretical guarantees.

Findings

SELCON outperforms existing methods in accuracy-efficiency trade-offs.

The objective function is shown to be monotone and alpha-submodular.

Experiments demonstrate SELCON's effectiveness across multiple datasets.

Abstract

Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this paper, our goal is to design an algorithm for selecting a subset of the training data, so that the model can be trained quickly, without significantly sacrificing on accuracy. More specifically, we focus on data subset selection for L2 regularized regression problems and provide a novel problem formulation which seeks to minimize the training loss with respect to both the trainable parameters and the subset of training data, subject to error bounds on the validation set. We tackle this problem using several technical innovations. First, we represent this problem with simplified constraints using the dual of the original training problem and show that the objective of this new representation is a monotone and alpha-submodular function, for a wide variety of modeling choices. Such properties lead us to develop SELCON, an efficient majorization-minimization algorithm for data subset selection, that admits an approximation guarantee even when the training provides an imperfect estimate of the trained model. Finally, our experiments on several datasets show that SELCON trades off accuracy and efficiency more effectively than the current state-of-the-art.