Refinements of Pinsker's inequality

By A. A. Fedotov, Peter Harremoës, Flemming Topsøe. 2003

193 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Electrical and Electronic Engineering

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Citations in the corpus

On the empirical estimation of integral probability metrics (2012, background): “[16] and references therein for more refined bounds between TV and KL.”
Rényi Divergence and Kullback-Leibler Divergence (2012, background): “Proof: We omit the proof for α = 1, which is the standard version of Pinsker’s inequality (see [52] for a survey of its history).”
On integral probability metrics, φ-divergences and binary classification (2009, background): “These bounds also translate as lower bounds on the KL-divergence through Pinsker’s inequality [36].”
On Pinsker's and Vajda's Type Inequalities for Csiszár's $f$ -Divergences (2006, background): “More recently, Topsøe showed in [15] that , while Fedotov et al. [2] have obtained a parametrization of the curve in terms of hyperbolic trigonometric functions and argue in [16] that the Taylor expansion of containing terms up to and including provides a lower bound for .”
Berry–Esseen bounds in the entropic central limit theorem (2011, background): “Moreover, by the Pinsker-Csiszár-Kullback inequality [11,13,17,21], the entropic distance dominates the total variation in the sense that D(X) ≥ 1 2 ‖FX − FZ‖(2)TV.”
On Divergences and Informations in Statistics and Information Theory (2006, methodology): “Decision-theoretic applications of -divergences can be found, e.g., in Kailath [27], Poor [43], LeCam [31], Read and Cressie [45], Clarke and Barron [9], Longo et al. [35], Torgersen [50], Österreicher and Vajda [41], Topsøe [49], and Fedotov et al. [18].”
On achievable rate regions for the Gaussian interference channel (2004, background): “6) One possible direction in trying to fix this problematic issue which is addressed in item 2) relies on recent improvements on Pinsker’s inequality [8].”
Information, Divergence and Risk for Binary Experiments (2009, background): “This “best possible Pinsker inequality” takes the form L(V ) := inf V (P,Q)=V KL(P,Q), V ∈ [0, 2) (83) Recently Fedotov et al. Fedotov et al. (2003) presented an implicit (parametric) version of the form (V (t), L(t))t∈R+ (84) V (t) = t ( 1− ( coth(t)− 1 t )2) , L(t) = log ( t sinh(t) ) + t…”
On the minimum f-divergence for given total variation (2006, background): “[6] or [5] for the relative entropy case).”
Properties of Classical and Quantum Jensen-Shannon Divergence (2008, background): “In [22] and [23] examples and techniques for the determination of such diagrams can be found.”
$f$ -Divergence Inequalities (2015, background): “(37) Remark 1: Different functions may lead to the same f -divergence for all (P,Q): if for an arbitrary b ∈ R, we have fb(t) = f0(t) + b (t− 1), t ≥ 0 (38) then Df0(P‖Q) = Dfb(P‖Q).”