Chernoff bound
E837386
The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Chernoff bound canonical | 4 |
| Chernoff bounds | 2 |
| Chernoff | 1 |
| Hoeffding inequality | 1 |
| multiplicative Chernoff bound | 1 |
| two-sided Chernoff bound | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10038310 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chernoff bound Context triple: [Chernoff information, relatedTo, Chernoff bound]
-
A.
Chebyshev inequalities
Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
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B.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
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C.
Chernoff information
Chernoff information is a measure in information theory and statistics that quantifies the exponential rate at which the error probability decays when optimally distinguishing between two probability distributions.
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D.
Barankin bound
The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
-
E.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chernoff bound Target entity description: The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.
-
A.
Chebyshev inequalities
Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
-
B.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
C.
Chernoff information
Chernoff information is a measure in information theory and statistics that quantifies the exponential rate at which the error probability decays when optimally distinguishing between two probability distributions.
-
D.
Barankin bound
The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
-
E.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concentration inequality
ⓘ
probabilistic inequality ⓘ tail bound ⓘ |
| appliesTo |
Bernoulli random variables
ⓘ
Poisson trials ⓘ binomial distribution ⓘ sum of independent random variables ⓘ |
| assumes |
bounded random variables in common forms
ⓘ
independence of random variables ⓘ |
| characterizes |
lower tail probability
ⓘ
upper tail probability ⓘ |
| comparedTo |
Chebyshev inequality
ⓘ
linked to:
Chebyshev inequalities
Hoeffding inequality ⓘ
linked to:
Azuma–Hoeffding inequality
Markov inequality ⓘ |
| field |
information theory
ⓘ
probability theory ⓘ statistics ⓘ theoretical computer science ⓘ |
| generalizes | Hoeffding inequality in some formulations ⓘ |
| gives | exponential upper bound on tail probability ⓘ |
| hasForm |
additive Chernoff bound
ⓘ
multiplicative Chernoff bound ⓘ
linked to:
Chernoff bound
two-sided Chernoff bound ⓘ
linked to:
Chernoff bound
|
| namedAfter | Herman Chernoff ⓘ |
| property | bounds decay exponentially in the number of trials ⓘ |
| provides | non-asymptotic tail estimates ⓘ |
| relatedTo |
Chernoff information
ⓘ
Cramér–Chernoff method ⓘ
linked to:
Cramér’s theorem in large deviations
Kullback–Leibler divergence ⓘ exponential Markov inequality ⓘ large deviations theory ⓘ moment generating function ⓘ |
| strongerThan |
Chebyshev inequality in many settings
ⓘ
linked to:
Chebyshev inequalities
Markov inequality in many settings ⓘ |
| typicalStatement |
P(X ≤ (1-δ)μ) ≤ exp(-μ g(δ)) for δ ∈ (0,1)
ⓘ
P(X ≥ (1+δ)μ) ≤ exp(-μ f(δ)) for δ > 0 ⓘ |
| usedFor |
bounding deviation from expectation
ⓘ
concentration of measure ⓘ derandomization ⓘ error analysis in communication systems ⓘ randomized algorithms analysis ⓘ sample complexity bounds in learning theory ⓘ |
| usedIn |
analysis of randomized algorithms for load balancing
ⓘ
coding theory ⓘ hashing and balls-into-bins analysis ⓘ hypothesis testing ⓘ network reliability analysis ⓘ queueing theory ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Chernoff bound Description of subject: The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Chernoff bound
linked to: Chernoff bound
linked to: Chernoff bound
linked to: Chernoff bound
linked to: Chernoff bound
linked to: Chernoff bound