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gptkbp:instanceOf
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gptkb:mathematical_concept
|
|
gptkbp:appliesTo
|
independent random variables
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|
gptkbp:describes
|
probability bound for sum of bounded independent random variables
|
|
gptkbp:field
|
gptkb:probability_theory
statistics
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Hoeffding's inequality
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gptkbp:namedAfter
|
gptkb:Wassily_Hoeffding
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gptkbp:provides
|
exponential bound on tail probabilities
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|
gptkbp:publicationYear
|
1963
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gptkbp:publishedIn
|
gptkb:Journal_of_the_American_Statistical_Association
|
|
gptkbp:relatedTo
|
gptkb:Bernstein_inequality
gptkb:Azuma's_inequality
gptkb:Chernoff_bound
|
|
gptkbp:sentence
|
For independent random variables X_i with a_i ≤ X_i ≤ b_i, P(S_n - E[S_n] ≥ t) ≤ exp(-2t^2/Σ(b_i-a_i)^2)
|
|
gptkbp:type
|
concentration inequality
|
|
gptkbp:usedFor
|
gptkb:empirical_risk_minimization
bounding generalization error
randomized algorithms analysis
|
|
gptkbp:usedIn
|
gptkb:machine_learning
learning theory
concentration inequalities
|
|
gptkbp:bfsParent
|
gptkb:Bernstein's_inequality
|
|
gptkbp:bfsLayer
|
6
|