The key highlights and insights of this work are:
The authors introduce a novel Auxiliary Distribution Method (ADM) to derive new upper bounds on the expected generalization error of supervised learning algorithms.
Using ADM, they derive bounds based on α-Jensen-Shannon (α-JS) divergence, which are always finite, unlike some existing mutual information-based bounds.
They also provide bounds based on α-Rényi divergence for 0 < α < 1, which can be finite even for deterministic supervised learning algorithms, in contrast to mutual information-based bounds.
The authors show how their bounds can be used to derive upper bounds on the excess risk of some learning algorithms and the generalization error under distribution mismatch between training and test data.
They outline conditions under which their proposed bounds might be tighter than earlier upper bounds.
The work provides a comprehensive analysis of generalization error bounds using various information-theoretic measures, offering new insights and tools for understanding the generalization properties of supervised learning algorithms.
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