mlsanityData to 14 Oct 2026

Relative Deviation Learning Bounds and Generalization with Unbounded Loss Functions

arXiv 1310.5796 ↗First posted 22 Oct 2013cs.LGcited by 15

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Abstract (arXiv)

We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of unbounded loss functions, under the assumption that a moment of the loss is bounded. These bounds are useful in the analysis of importance weighting and other learning tasks such as unbounded regression.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 Oct 2013.

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Citing papers per year: 2021: 6; 2022: 2; 2023: 3; 2024: 2; 2025: 1; 2026: 1.

15 papers.

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  1. 2021Simple and near-optimal algorithms for hidden stratification and multi-group learningcited by 28
  2. 2021On the Convergence of Step Decay Step-Size for Stochastic Optimizationcited by 21
  3. 2022Information-Theoretic Analysis of Unsupervised Domain Adaptationcited by 15
  4. 2022Differentially Private Learning with Margin Guaranteescited by 7
  5. 2023Best-Effort Adaptationcited by 7
  6. 2024Generalization and Robustness of the Tilted Empirical Riskcited by 4
  7. 2024Transformation-Invariant Learning and Theoretical Guarantees for OOD Generalizationcited by 4
  8. 2021Bandwidth-based Step-Sizes for Non-Convex Stochastic Optimizationcited by 2
  9. 2021Some Hoeffding- and Bernstein-type Concentration Inequalitiescited by 1
  10. 2021Conditional Linear Regression for Heterogeneous Covariancescited by 1
  11. 2023Distribution-free Deviation Bounds and The Role of Domain Knowledge in Learning via Model Selection with Cross-validation Risk Estimationcited by 1
  12. 2023Uniform Risk Bounds for Learning with Dependent Data Sequencescited by 1
3 more
  1. 2025Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Methodcited by 1
  2. 2026Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budgetcited by 1
  3. 2021Improving Generalization Bounds for VC Classes Using the Hypergeometric Tail Inversioncited by 0