The Randomness of Input Data Spaces is an A Priori Predictor for Generalization
This work addresses the challenge of understanding generalization in machine learning, particularly for binary classification, but it is incremental as it builds on existing concepts of data distribution properties.
The paper tackles the problem of predicting generalization error in deep neural networks by analyzing the randomness of input data spaces, finding a high correlation between measured randomness and generalization error across synthetic tasks and image classification benchmarks.
Over-parameterized models can perfectly learn various types of data distributions, however, generalization error is usually lower for real data in comparison to artificial data. This suggests that the properties of data distributions have an impact on generalization capability. This work focuses on the search space defined by the input data and assumes that the correlation between labels of neighboring input values influences generalization. If correlation is low, the randomness of the input data space is high leading to high generalization error. We suggest to measure the randomness of an input data space using Maurer's universal. Results for synthetic classification tasks and common image classification benchmarks (MNIST, CIFAR10, and Microsoft's cats vs. dogs data set) find a high correlation between the randomness of input data spaces and the generalization error of deep neural networks for binary classification problems.