Towards Optimal Neural Networks: the Role of Sample Splitting in Hyperparameter Selection
This provides theoretical justification for a common practice in neural network training, though it appears incremental.
The paper investigates why sample splitting works for hyperparameter selection in neural networks, showing that optimal hyperparameters from sample splitting asymptotically minimize prediction risk.
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.