Related papers: An information diffusion Fano inequality
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…
In this note, we present a version of Hoeffding's inequality in a continuous-time setting, where the data stream comes from a uniformly ergodic diffusion process. Similar to the well-studied case of Hoeffding's inequality for discrete-time…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verd\'{u} on…
In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.
The aim of this paper is to analyze the weighted KyFan inequality proposed in [11]. A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an…
The strengthened data processing inequality have been proved. The general theory have been illustrated on the simple example.
In this paper we consider Levin's notion of mutual information in infinite 0-1-sequences, as defined in [Leonid Levin. Laws of Information Conservation (Nongrowth) and Aspects of the Foundation of Probability Theory. Problems of information…
We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum…
We derive a general information-theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement…
We investigate the propagation of information through one-dimensional quantum chains in fluctuating external fields. We find that information propagation is suppressed, but in a quite different way compared to the situation with static…
We develop an information-theoretic approach to isoperimetric inequalities based on entropy dissipation under heat flow. By viewing diffusion as a noisy information channel, we measure how mutual information about set membership decays over…
Two new proofs of the Fisher information inequality (FII) using data processing inequalities for mutual information and conditional variance are presented.
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences.…
We extend present Shannon's static statistical information theory to dynamic processes and establish a dynamic statistical information theory. We derive the nonlinear evolution equations of dynamic information density and dynamic…
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…
A conditional version of Sibson's $\alpha$-information is defined using a simple closed-form "log-expectation" expression, which satisfies important properties such as consistency, uniform expansion, and data processing inequalities. This…
We present a theory for Fano interference in light scattering by individual obstacle, based on a temporal coupled-mode formalism. This theory is applicable for obstacles that are much smaller than the incident wavelength, or for systems…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…