Related papers: A note on insufficiency and the preservation of Fi…
In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
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,…
Symmetric alpha-stable (S alpha S) distributions with alpha<2 lack finite classical Fisher information. Building on Johnson's framework, we define Mixed Fractional Information (MFI) via the initial rate of relative entropy dissipation…
To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different…
The Fisher information matrix provides a way to measure the amount of information given observed data based on parameters of interest. Many applications of the FIM exist in statistical modeling, system identification, and parameter…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the…
Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold…
We show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty…
We study here the difference between quantum statistical treatments and semi-classical ones, using as the main research tool a semi-classical, shift-invariant Fisher information measure built up with Husimi distributions. Its semi-classical…
Logarithmic score and information divergence appear in both information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to the use…
We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…
We consider kinetic models for Fermi-Dirac-like particles obeying the exclusion principle. A generalized notion of Fisher information, tailored to kinetic equations of Fermi-Dirac-Fokker-Planck type, is introduced via the associated entropy…
We estimate a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the transition intensity matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes…
We consider the behaviour of the Fisher information of scaled sums of independent and identically distributed random variables in the Central Limit Theorem regime. We show how this behaviour can be related to the second-largest non-trivial…
Symmetry breaking underlies diverse phenomena from phase transitions in condensed matter to fundamental interactions in gauge theories. Despite many proposed indicators, a general quantification of symmetry breaking that is faithful,…
A robust prediction model invoking the Takens embedding theorem, whose \textit{working hypothesis} is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz,…
Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…
In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…