Towards Optimal Neural Networks: the Role of Sample Splitting in Hyperparameter Selection

TL;DR

This paper develops a new theoretical understanding of how sample splitting for hyperparameter tuning can lead neural networks to asymptotically minimize prediction risk, supported by extensive experiments.

Contribution

It introduces a novel theory explaining the effectiveness of sample splitting in hyperparameter selection for neural networks, highlighting its role in asymptotic risk minimization.

Findings

Sample splitting helps select hyperparameters that asymptotically minimize prediction risk.

The proposed theory is validated through extensive experiments across various scenarios.

Results demonstrate the practical effectiveness of the theoretical insights.

Abstract

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization performance, have concurrently made significant strides. In this paper, we construct a novel theory for understanding the effectiveness of neural networks, which offers a perspective distinct from prior research. Specifically, we explore the rationale underlying a common practice during the construction of neural network models: sample splitting. Our findings indicate that the optimal hyperparameters derived from sample splitting can enable a neural network model that asymptotically minimizes the prediction risk. We conduct extensive experiments across different application scenarios and network architectures, and the results manifest our theory's effectiveness.