Stein’s density approach and information inequalities

By Christophe Ley, Yvik Swan. 2012

75 citations recorded by the source corpus.

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein identity which we use to derive information inequalities in terms of what we call the "generalized Fisher information distance". We provide explicit bounds on the constants appearing in these inequalities for several important cases. We conclude with a comparison between our results and known results in the Gaussian case, hereby improving on several known inequalities from the literature.

Subfields: Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “Lemma 2.3 (Ley & Swan (2013)) .”
Density Estimation in Infinite Dimensional Exponential Families (2013, background): “, ∂ log p ( x ) ∂x d Moreover, convergence in Fisher divergence is a stronger form of convergence than that in KL, total variation and Hellinger distances ([23, Lemmas E.2 & E.3], [25, Corollary 5.1]).”
Stein's method for comparison of univariate distributions (2014, methodology): “See also [30, 58, 28, 65] for computations under quite general assumptions on the density of X1.”
Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models (2020, unknown): “(Ley et al., 2013) Suppose p, q are probability densities deﬁned on R n and f : R n → R m is a function satisfying the Stein regular condition w.r.t. p, q , we deﬁne as functions of h w.r.t. p θ ( h | v ) , q φ ( h | v ) are bounded w.r.t. v , θ and φ , (3) ∇ v log ˜ p θ ( v , h ) and ∇ θ log ˜ p θ…”