Csiszár f-divergence
E841827
Csiszár f-divergence is a broad class of statistical distance measures between probability distributions defined via convex functions, encompassing many well-known divergences such as Kullback–Leibler and total variation as special cases.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Csiszár f-divergence canonical | 1 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
information theoretic quantity
ⓘ
statistical distance measure ⓘ statistical divergence ⓘ |
| alsoKnownAs |
Csiszár–Morimoto divergence
NERFINISHED
ⓘ
f-divergence NERFINISHED ⓘ |
| appliesTo |
continuous probability distributions
ⓘ
discrete probability distributions ⓘ probability measures on measurable spaces ⓘ |
| basedOn | convex function on positive reals ⓘ |
| codomain | nonnegative real numbers ⓘ |
| conditionOn | f(1) = 0 ⓘ |
| definedBetween | probability distributions ⓘ |
| domain | pairs of probability measures ⓘ |
| equalsZeroIfAndOnlyIf | two distributions are equal almost surely ⓘ |
| field |
information theory
ⓘ
machine learning ⓘ probability theory ⓘ statistics ⓘ |
| generalizes |
Hellinger distance
NERFINISHED
ⓘ
Itakura–Saito divergence NERFINISHED ⓘ Jensen–Shannon divergence NERFINISHED ⓘ Kullback–Leibler divergence NERFINISHED ⓘ Neyman chi-squared divergence ⓘ Pearson chi-squared divergence NERFINISHED ⓘ reverse Kullback–Leibler divergence ⓘ total variation distance ⓘ |
| hasSpecialCase |
Hellinger distance via f(t) = (
√t - 1
)^2
ⓘ
Kullback–Leibler divergence via f(t) = t log t ⓘ reverse Kullback–Leibler divergence via f(t) = -log t ⓘ total variation distance via f(t) = 0.5|t-1| ⓘ |
| introducedBy | Imre Csiszár NERFINISHED ⓘ |
| introducedInContextOf | information measures of probability distributions ⓘ |
| namedAfter | Imre Csiszár NERFINISHED ⓘ |
| nonNegative | true ⓘ |
| property |
convex in each argument under suitable parametrization
ⓘ
does not satisfy triangle inequality in general ⓘ not symmetric in general ⓘ |
| relatedTo |
Bregman divergence
ⓘ
f-information ⓘ |
| requires |
absolute continuity of one measure with respect to the other for integral form
ⓘ
convex function ⓘ |
| satisfies | data processing inequality ⓘ |
| usedFor |
density ratio estimation
ⓘ
distributional robustness ⓘ generative modeling ⓘ goodness-of-fit testing ⓘ hypothesis testing ⓘ information geometry ⓘ robust statistics ⓘ variational inference ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.