mlsanityData to 7 Oct 2026

Proofs for Folklore Theorems on the Radon-Nikodym Derivative

arXiv 2501.18374 ↗First posted 30 Jan 2025cs.IT math.HO math.ITcited by 4

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Abstract (arXiv)

In this technical report, rigorous statements and formal proofs are presented for both foundational and advanced folklore theorems on the Radon-Nikodym derivative. The cases of conditional and marginal probability measures are carefully considered, which leads to an identity involving the sum of mutual and lautum information suggesting a new interpretation for such a sum.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 7 of its 35 references that are in the map. First posted on arXiv 30 Jan 2025.

Builds on

7 of 35 references.

References · 7

  1. 2020Optimal Bounds between f-Divergences and Integral Probability Metricscited by 27
  2. 2022Empirical Risk Minimization with Relative Entropy Regularizationcited by 13
  3. 2024An Information-Theoretic Approach to Generalization Theorycited by 9
  4. 2022f-divergences and their applications in lossy compression and bounding generalization errorcited by 7
  5. 2024Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergencescited by 6
  6. 2024Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimizationcited by 6
  7. 2024The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithmscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Variations on the Expectation due to Changes in the Probability Measurecited by 3
  2. 2026Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithmscited by 2
  3. 2026Empirical Risk Minimization with f-Divergence Regularizationcited by 0
  4. 2026Machine Unlearning for Gibbs Supervised Learning Algorithmscited by 0