Tighter Information-Theoretic Generalization Bounds via a Novel Class of Change of Measure Inequalities

• URL: http://arxiv.org/abs/2602.07999v2
• Date: Tue, 10 Feb 2026 05:48:16 GMT
• Title: Tighter Information-Theoretic Generalization Bounds via a Novel Class of Change of Measure Inequalities
• Authors: Yanxiao Liu, Yijun Fan, Deniz Gündüz,
• Abstract summary: We provide change of measure inequalities in terms of a broad family of information measures, including $f$-divergences and $2$-divergence as special cases.<n>We then embed these inequalities into the analysis of generalization error for learning algorithms, novel and tighter high-probability information-theoretic bounds, while also recovering several best-known results via simplified analyses.
• Score: 42.8036344206885
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a novel class of change of measure inequalities via a unified framework based on the data processing inequality for $f$-divergences, which is surprisingly elementary yet powerful enough to yield tighter inequalities. We provide change of measure inequalities in terms of a broad family of information measures, including $f$-divergences (with Kullback-Leibler divergence and $χ^2$-divergence as special cases), Rényi divergence, and $α$-mutual information (with maximal leakage as a special case). We then embed these inequalities into the analysis of generalization error for stochastic learning algorithms, yielding novel and tighter high-probability information-theoretic generalization bounds, while also recovering several best-known results via simplified analyses. A key advantage of our framework is its flexibility: it readily adapts to a range of settings, including the conditional mutual information framework, PAC-Bayesian theory, and differential privacy mechanisms, for which we derive new generalization bounds.

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