WebbWhen the prior probabilities are equal, that is P ( A) = P ( B) = 1 2, (1) reduces to the expression involving the total variation distance between probability distributions … Webb10 jan. 2024 · In this note we propose a simplified approach to recent reverse Pinsker inequalities due to O. Binette. More precisely, we give direct proofs of optimal variational …
Simple proof of Pinsker
In information theory, Pinsker's inequality, named after its inventor Mark Semenovich Pinsker, is an inequality that bounds the total variation distance (or statistical distance) in terms of the Kullback–Leibler divergence. The inequality is tight up to constant factors. Visa mer Pinsker's inequality states that, if $${\displaystyle P}$$ and $${\displaystyle Q}$$ are two probability distributions on a measurable space $${\displaystyle (X,\Sigma )}$$, then Visa mer Pinsker first proved the inequality with a greater constant. The inequality in the above form was proved independently by Kullback, Csiszár, and Kemperman. Visa mer • Thomas M. Cover and Joy A. Thomas: Elements of Information Theory, 2nd edition, Willey-Interscience, 2006 • Nicolo Cesa-Bianchi and Gábor Lugosi: Prediction, Learning, and Games, Cambridge University Press, 2006 Visa mer WebbThe Csiszár-Kullback inequality (or Csiszár-Kullback-Pinsker inequality, or Pinsker-type inequality) originally derived in these papers by Csiszár and Kullback building on … erich stephany
BEST PINSKER BOUND EQUALS TAYLOR POLYNOMIAL OF …
Webb6 juni 2009 · We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f … WebbThis shows that it suffices to prove the binary case of Pinsker's, which is just a matter of proving a simple inequality: (3) 2 ( − q) 2 ≤ p log p q + ( 1 −) log 1 − p 1 − q The cases where either is in 0, 1 are easily checked , so we can assume ,,) . Webboptimal “reverse Pinsker inequalities” for any f-divergence. This refines or shows the optimality of previously best known inequalities while avoiding arguments that are tuned … erichs towing