On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities¶
Vapnik, V. N., & Chervonenkis, A. Y. (1971). On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities. Theory of Probability & Its Applications, 16(2), 264-280.
Cited by¶
4 citations across 4 artifacts.
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Primes¶
- Inductive Reasoning
- Contemporary machine-learning theory, rooted in Valiant's PAC framework and Vapnik-Chervonenkis dimension analysis
This sourceVapnik Chervonenkis VC dimension generalization bounds learning theory.
- Contemporary machine-learning theory, rooted in Valiant's PAC framework and Vapnik-Chervonenkis dimension analysis
- Law of Large Numbers
- Machine learning. Empirical risk minimization justifies choosing a model by its average loss on a training sample — but the required law must hold uniformly over the whole hypothesis class rather than pointwise for a fixed predictor, which is why capacity control and held-out evaluation are necessary.
This sourceEstablishes that empirical frequencies must converge uniformly over the whole class of events, not pointwise for a fixed one, which is the condition empirical risk minimization actually needs.
- Machine learning. Empirical risk minimization justifies choosing a model by its average loss on a training sample — but the required law must hold uniformly over the whole hypothesis class rather than pointwise for a fixed predictor, which is why capacity control and held-out evaluation are necessary.
- Overfitting
This sourceVapnik Chervonenkis VC dimension generalization bounds learning theory.
- Requisite Variety
- … project; modern applications in enterprise architecture, agile team design, network-centric organizations), machine learning and statistics (model capacity must match data complexity — under-capacity models fail, over-capacity models overfit; hypothesis-class VC dimension bounds as requisite-variety analogs)
This sourceVapnik-Chervonenkis VC dimension hypothesis class complexity bounds.
- … project; modern applications in enterprise architecture, agile team design, network-centric organizations), machine learning and statistics (model capacity must match data complexity — under-capacity models fail, over-capacity models overfit; hypothesis-class VC dimension bounds as requisite-variety analogs)
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