Jensen–Shannon divergence
E837388
distance-like measure between probability distributions
information-theoretic measure
statistical divergence
Jensen–Shannon divergence is a symmetrized and smoothed measure of dissimilarity between probability distributions, widely used in information theory and machine learning.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Jensen–Shannon divergence canonical | 4 |
| Jensen–Shannon distance | 1 |
| Jensen–Shannon distance (square root form) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10038331 — 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: Jensen–Shannon divergence Context triple: [Chernoff information, comparedWith, Jensen–Shannon divergence]
-
A.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
B.
Bhattacharyya distance
Bhattacharyya distance is a statistical measure of similarity between two probability distributions, often used in pattern recognition and classification to quantify their overlap.
-
C.
Rényi divergence
Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
-
D.
Tsallis divergence
Tsallis divergence is a generalized measure of statistical distance between probability distributions derived from Tsallis entropy, often used in nonextensive statistical mechanics and information theory.
-
E.
Hellinger distance
Hellinger distance is a statistical measure of dissimilarity between probability distributions, derived from the Euclidean distance between their square-root densities and widely used in probability theory and information geometry.
- 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: Jensen–Shannon divergence Target entity description: Jensen–Shannon divergence is a symmetrized and smoothed measure of dissimilarity between probability distributions, widely used in information theory and machine learning.
-
A.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
B.
Bhattacharyya distance
Bhattacharyya distance is a statistical measure of similarity between two probability distributions, often used in pattern recognition and classification to quantify their overlap.
-
C.
Rényi divergence
Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
-
D.
Tsallis divergence
Tsallis divergence is a generalized measure of statistical distance between probability distributions derived from Tsallis entropy, often used in nonextensive statistical mechanics and information theory.
-
E.
Hellinger distance
Hellinger distance is a statistical measure of dissimilarity between probability distributions, derived from the Euclidean distance between their square-root densities and widely used in probability theory and information geometry.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
distance-like measure between probability distributions
ⓘ
information-theoretic measure ⓘ statistical divergence ⓘ |
| alsoKnownAs |
Jensen–Shannon distance (square root form)
ⓘ
linked to:
Jensen–Shannon divergence
|
| basedOn | Kullback–Leibler divergence ⓘ |
| bounded | true ⓘ |
| canBeExpressedUsingEntropy | true ⓘ |
| definedFor | pairs of probability distributions ⓘ |
| definedOn |
continuous probability distributions (via densities)
ⓘ
discrete probability distributions ⓘ |
| entropyForm | JSD(P‖Q) = H(M) − 1/2 H(P) − 1/2 H(Q) ⓘ |
| field |
information theory
ⓘ
machine learning ⓘ probability theory ⓘ statistics ⓘ |
| formula | JSD(P‖Q) = 1/2 KL(P‖M) + 1/2 KL(Q‖M) ⓘ |
| generalizedDefinition | JSD({P_i}, {w_i}) = H(∑ w_i P_i) − ∑ w_i H(P_i) ⓘ |
| generalizesTo | more than two distributions ⓘ |
| isConvexInEachArgument | true ⓘ |
| isDefinedWhenSupportsDiffer | true ⓘ |
| isFdivergence | true ⓘ |
| isFinite | true ⓘ |
| isJointlyConvex | true ⓘ |
| isMetricWhenSquareRootTaken | true ⓘ |
| isRelatedTo | Shannon entropy ⓘ |
| isRobustToSupportMismatchComparedTo | Kullback–Leibler divergence ⓘ |
| isSmoothedVersionOf | Kullback–Leibler divergence ⓘ |
| isSquareOfMetric | true ⓘ |
| isSymmetric | true ⓘ |
| isSymmetrizationOf | Kullback–Leibler divergence ⓘ |
| isWidelyUsedAs | measure of dissimilarity between probability distributions ⓘ |
| isZeroIffDistributionsEqual | true ⓘ |
| logarithmBase | commonly base 2 ⓘ |
| metricName |
Jensen–Shannon distance
ⓘ
linked to:
Jensen–Shannon divergence
|
| mixtureDistributionDefinition | M = 1/2 (P + Q) for two distributions P and Q ⓘ |
| nonNegative | true ⓘ |
| requires | probability distributions with total mass 1 ⓘ |
| satisfiesTriangleInequalityWhenSquareRootTaken | true ⓘ |
| unit |
bits (for base-2 logarithm)
ⓘ
nats (for natural logarithm) ⓘ |
| upperBoundValue | log 2 (for base-2 logarithm and two distributions) ⓘ |
| usedIn |
GAN training objectives (via JS-based losses)
ⓘ
bioinformatics sequence comparison ⓘ clustering of probability distributions ⓘ distributional clustering of words ⓘ document similarity ⓘ generative model evaluation ⓘ natural language processing ⓘ topic modeling evaluation ⓘ |
| usesMixtureDistribution | true ⓘ |
| weightConstraints | weights w_i are nonnegative and sum to 1 ⓘ |
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: Jensen–Shannon divergence Description of subject: Jensen–Shannon divergence is a symmetrized and smoothed measure of dissimilarity between probability distributions, widely used in information theory and machine learning.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Jensen–Shannon divergence
linked to: Jensen–Shannon divergence