mlsanityData to 14 Oct 2026

On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation

arXiv 2306.12380 ↗First posted 21 Jun 2023cs.LG cs.IT math.ITcited by 10

Not on the map. Why?

Abstract (arXiv)

The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the GA is obtained in closed form. In this case, sensitivity is the performance difference with respect to an arbitrary alternative algorithm. This description enables the development of explicit expressions involving the training errors and test errors of GAs trained with different datasets. Using these tools, dataset aggregation is studied and different figures of merit to evaluate the generalization capabilities of GAs are introduced. For particular sizes of such datasets and parameters of the GAs, a connection between Jeffrey's divergence, training and test errors is established.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 16 of its 36 references that are in the map. First posted on arXiv 21 Jun 2023.

Builds on

16 of 36 references.

References · 16

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,669
  2. 2017Information-theoretic analysis of generalization capability of learning algorithmscited by 303
  3. 2015Statistical physics of inference: Thresholds and algorithmscited by 128
  4. 2015On the properties of variational approximations of Gibbs posteriorscited by 121
  5. 2015How much does your data exploration overfit? Controlling bias via information usagecited by 95
  6. 2020Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithmscited by 89
  7. 2018Chaining Mutual Information and Tightening Generalization Boundscited by 65
  8. 2019Generalization Error Bounds Via R'enyi-, f-Divergences and Maximal Leakagecited by 48
  9. 2020PAC-Bayes unleashed: generalisation bounds with unbounded lossescited by 43
  10. 2021Tighter expected generalization error bounds via Wasserstein distancecited by 43
  11. 2020Jensen-Shannon Information Based Characterization of the Generalization Error of Learning Algorithmscited by 19
  12. 2019Still no free lunches: the price to pay for tighter PAC-Bayes boundscited by 14
4 more
  1. 2022Tighter Expected Generalization Error Bounds via Convexity of Information Measurescited by 11
  2. 2022Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysiscited by 8
  3. 2019Chaining Meets Chain Rule: Multilevel Entropic Regularization and Training of Neural Netscited by 6
  4. 2023Analysis of the Relative Entropy Asymmetry in the Regularization of Empirical Risk Minimizationcited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 2; 2026: 4.

10 papers.

  1. 2023Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measurecited by 7
  2. 2024Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergencescited by 6
  3. 2024Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimizationcited by 6
  4. 2024The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithmscited by 5
  5. 2025Variations on the Expectation due to Changes in the Probability Measurecited by 3
  6. 2026Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithmscited by 2
  7. 2025A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularizationcited by 1
  8. 2026Empirical Risk Minimization with f-Divergence Regularizationcited by 0
  9. 2026Equivalence Between Nested Gibbs Measures and Log-Linear Combinations of Gibbs Measurescited by 0
  10. 2026Machine Unlearning for Gibbs Supervised Learning Algorithmscited by 0