Tighter Expected Generalization Error Bounds via Convexity of Information Measures
This provides incremental improvements in theoretical understanding of generalization error bounds for machine learning researchers.
The paper tackles the problem of deriving tighter generalization error bounds for machine learning algorithms by proposing novel upper bounds based on the average joint distribution between the hypothesis and training samples, using information measures like Wasserstein distance and total variation distance. The results show these bounds are tighter than existing counterparts due to the convexity of the measures, with an example provided to demonstrate this tightness.
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each input training sample. Multiple generalization error upper bounds based on different information measures are provided, including Wasserstein distance, total variation distance, KL divergence, and Jensen-Shannon divergence. Due to the convexity of the information measures, the proposed bounds in terms of Wasserstein distance and total variation distance are shown to be tighter than their counterparts based on individual samples in the literature. An example is provided to demonstrate the tightness of the proposed generalization error bounds.