Related papers: On weighted Fisher information matrix properties
The notion of weighted quantum entropy is reviewed and considered for bipartite and noncomposite quantum systems. The known for the weighted entropy information inequality (subadditivity condition) is extended to the case of indivisible…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for…
The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…
A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…
We produce a series of results extending information-theoretical inequalities (discussed by Dembo--Cover--Thomas in 1989-1991) to a weighted version of entropy. The resulting inequalities involve the Gaussian weighted entropy; they imply a…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
We establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions. In the first part of the paper, we derive volume bounds for convex bodies using generalized…
We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…
We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized $q$-Gaussian…
We work out the general theory of one-parameter families of partial entanglement properties and the resulting entanglement depth-like quantities. Special cases of these are the depth of partitionability, the depth of producibility (or…
Two new proofs of the Fisher information inequality (FII) using data processing inequalities for mutual information and conditional variance are presented.
Basic general properties are considered for the Fisher-type information involving higher order derivatives. They are used to explore various properties of probability densities and to derive Stam-type inequalities.
We show that the weak equivalence principle (WEP) is violated for a quantum particle in a gravitational wave (GW) background, in the sense that extra mass information can be extracted in the presence of the GW. We quantify the degree of…
One of the most popular methods for continual learning with deep neural networks is Elastic Weight Consolidation (EWC), which involves computing the Fisher Information. The exact way in which the Fisher Information is computed is however…
In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…
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…