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A survey on scenario theory, complexity and compression-based learning and generalization

IEEE transaction on neural networks and learning systems, 2023-09, Vol.103, p.1-15

Distributed under a Creative Commons Attribution 4.0 International License ;ISSN: 2162-237X ;EISSN: 2162-2388 ;DOI: 10.1109/TNNLS.2023.3308828

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  • Title:
    A survey on scenario theory, complexity and compression-based learning and generalization
  • Author: rocchetta, roberto ; Mey, Alexander ; Oliehoek, Frans
  • Subjects: Computer Science ; Statistics
  • Is Part Of: IEEE transaction on neural networks and learning systems, 2023-09, Vol.103, p.1-15
  • Description: This work investigates formal generalization error bounds that apply to support vector machines in realizable and agnostic learning problems. We focus on recently observed parallels between PAC-learning (probably approximately correct learning) bounds, like compression and complexity-based bounds, and novel error guarantees derived within scenario theory. Scenario theory provides non-asymptotic and distributionalfree error bounds for models trained by solving data-driven decision-making problems. Relevant theorems and assumptions are reviewed and discussed. We propose a numerical comparison of the tightness and effectiveness of theoretical error bounds for support vector classifiers trained on several randomized experiments from thirteen real-life problems. This analysis allows for a fair comparison of different approaches from both conceptual and experimental standpoints. Based on the numerical results, we argue that the error guarantees derived from scenario theory are often tighter for realizable problems and always yield informative results, i.e., probability bounds tighter than a vacuous [0,1] interval. This work promotes scenario theory as an alternative tool for model selection, structural-risk minimization and generalization error analysis of support vector machines. In this way, we hope to bring the communities of scenario and statistical learning theory closer so that they can benefit from each other's insights.
  • Publisher: IEEE
  • Language: French
  • Identifier: ISSN: 2162-237X
    EISSN: 2162-2388
    DOI: 10.1109/TNNLS.2023.3308828
  • Source: Hyper Article en Ligne (HAL) (Open Access)
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