Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
sum of independent random variables
|
| gptkbp:field |
gptkb:probability_theory
mathematical analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Bernstein's inequality
|
| gptkbp:namedAfter |
gptkb:Sergei_Bernstein
|
| gptkbp:provides |
upper bound on probability of large deviations
|
| gptkbp:publishedIn |
1924
|
| gptkbp:relatedTo |
gptkb:Hoeffding's_inequality
gptkb:Azuma's_inequality gptkb:Chernoff_bound |
| gptkbp:sentence |
For independent zero-mean random variables bounded by M, the probability that their sum exceeds t is bounded by exp(-t^2/(2σ^2 + 2Mt/3)).
|
| gptkbp:type |
concentration inequality
|
| gptkbp:usedIn |
gptkb:machine_learning
gptkb:empirical_process_theory statistics |
| gptkbp:bfsParent |
gptkb:Joseph_Bernstein
|
| gptkbp:bfsLayer |
5
|