Data splitting improves statistical performance in overparametrized regimes

TL;DR

This paper demonstrates that data splitting acts as a regularizer in overparametrized ridgeless regression, enhancing statistical performance and computational efficiency across finite and infinite-dimensional settings.

Contribution

It introduces a unified framework showing data splitting's regularizing effect in overparametrized regimes, improving both accuracy and efficiency.

Findings

Data splitting improves statistical performance in overparametrized models.

Regularizing effect of data splitting reduces computational complexity.

Effect demonstrated in both finite and infinite-dimensional settings.

Abstract

While large training datasets generally offer improvement in model performance, the training process becomes computationally expensive and time consuming. Distributed learning is a common strategy to reduce the overall training time by exploiting multiple computing devices. Recently, it has been observed in the single machine setting that overparametrization is essential for benign overfitting in ridgeless regression in Hilbert spaces. We show that in this regime, data splitting has a regularizing effect, hence improving statistical performance and computational complexity at the same time. We further provide a unified framework that allows to analyze both the finite and infinite dimensional setting. We numerically demonstrate the effect of different model parameters.