mlsanityData to 7 Oct 2026

Hypothesis Set Stability and Generalization

arXiv 1904.04755 ↗First posted 9 Apr 2019cs.LG stat.MLcited by 23

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Abstract (arXiv)

We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization bound for data-dependent hypothesis sets expressed in terms of a notion of hypothesis set stability and a notion of Rademacher complexity for data-dependent hypothesis sets that we introduce. This bound admits as special cases both standard Rademacher complexity bounds and algorithm-dependent uniform stability bounds. We also illustrate the use of these learning bounds in the analysis of several scenarios.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Apr 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 4; 2024: 4; 2025: 4; 2026: 2.

23 papers.

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  1. 2022Topology-aware Generalization of Decentralized SGDcited by 37
  2. 2021Stability and Generalization of Stochastic Gradient Methods for Minimax Problemscited by 35
  3. 2021Churn Reduction via Distillationcited by 17
  4. 2023Generalization Bounds with Data-dependent Fractal Dimensionscited by 15
  5. 2024Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Setscited by 9
  6. 2022Exploring the Algorithm-Dependent Generalization of AUPRC Optimization with List Stabilitycited by 8
  7. 2022Generalization Properties of Retrieval-based Modelscited by 5
  8. 2022On the Algorithmic Stability and Generalization of Adaptive Optimization Methodscited by 5
  9. 2023Sample-Conditioned Hypothesis Stability Sharpens Information-Theoretic Generalization Boundscited by 5
  10. 2023Generalization Guarantees via Algorithm-dependent Rademacher Complexitycited by 4
  11. 2024The Price of Implicit Bias in Adversarially Robust Generalizationcited by 4
  12. 2022Boosting the Confidence of Generalization for L2-Stable Randomized Learning Algorithmscited by 3
11 more
  1. 2023On the Stability and Generalization of Triplet Learningcited by 2
  2. 2024Stability and Sharper Risk Bounds with Convergence Rate tildeO(1/n2)cited by 2
  3. 2022Teacher Guided Training: An Efficient Framework for Knowledge Transfercited by 1
  4. 2025Stability, Complexity and Data-Dependent Worst-Case Generalization Boundscited by 1
  5. 2025Revisiting Knowledge Distillation: The Hidden Role of Dataset Sizecited by 1
  6. 2026Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithmscited by 1
  7. 2021Improved Learning Rates for Stochastic Optimizationcited by 0
  8. 2024Understanding Generalization of Federated Learning: the Trade-off between Model Stability and Optimizationcited by 0
  9. 2025A Bootstrap Perspective on Stochastic Gradient Descentcited by 0
  10. 2025Disentangled and Distilled Encoder for Out-of-Distribution Reasoning with Rademacher Guaranteescited by 0
  11. 2026Generalization at the Edge of Stabilitycited by 0