The Minimum Increment of f-Divergences Given Total Variation Distancesстатья
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Дата последнего поиска статьи во внешних источниках: 3 мая 2017 г.
Аннотация:Let (Pi,Qi), i = 0, 1, be two pairs of probability measures defined on measurable
spaces (Ωi,Fi) respectively. Assume that the pair (P1,Q1) is more informative than (P0,Q0) for
testing problems. This amounts to say that If (P1,Q1) ≥ If (P0,Q0), where If (·, ·) is an arbitrary fdivergence.
We find a precise lower bound for the increment of f-divergences If (P1,Q1) − If (P0,Q0)
provided that the total variation distances Q1 − P1 and Q0 − P0 are given. This optimization
problem can be reduced to the case where P1 and Q1 are defined on the space consisting of four
points, and P0 and Q0 are obtained from P1 and Q1 respectively by merging two of these four points.
The result includes the well-known lower and upper bounds for If (P,Q) given Q − P.