Chernoff bound

E837386

concentration inequality probabilistic inequality tail bound

The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.

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All labels observed (2)

Label	Occurrences
Chernoff bound canonical	2
Hoeffding inequality	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.
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
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 NERFINISHED ⓘ Hoeffding inequality NERFINISHED ⓘ Markov inequality NERFINISHED ⓘ
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 NERFINISHED ⓘ two-sided Chernoff bound NERFINISHED ⓘ
namedAfter	Herman Chernoff NERFINISHED ⓘ
property	bounds decay exponentially in the number of trials ⓘ
provides	non-asymptotic tail estimates ⓘ
relatedTo	Chernoff information NERFINISHED ⓘ Cramér–Chernoff method NERFINISHED ⓘ Kullback–Leibler divergence NERFINISHED ⓘ exponential Markov inequality ⓘ large deviations theory ⓘ moment generating function ⓘ
strongerThan	Chebyshev inequality in many settings NERFINISHED ⓘ 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

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Chernoff information → relatedTo → Chernoff bound ⓘ

Bernstein inequalities → relatedTo → Chernoff bound ⓘ

this entity surface form: Hoeffding inequality