Related papers: Statistical Meaning of Mean Functions
In recent years, in quantum information theory, there has been a remarkable development in the general theoretical framework for studying symmetry in dynamics. This development, called resource theory of asymmetry, is expected to have a…
For linear mixed models with co-variance matrices which are not linearly dependent on variance component parameters, we prove that the average of the observed information and the Fisher information can be split into two parts. The essential…
In order to formulate the Fundamental Theorem of Natural Selection, Fisher defined the average excess and average effect of a gene substitution. Finding these notions to be somewhat opaque, some authors have recommended reformulating…
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…
We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…
On the set $\mathcal M$ of mean functions the symmetric mean of $M$ with respect to mean $M_0$ can be defined in several ways. The first one is related to the group structure on $\mathcal M$ and the second one is defined trough Gauss'…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
With the help of the coherent states' basis we establish an interesting connection among i) the so-called Wehrl entropy, ii) Fisher's information measure $I$, and iii) the canonical ensemble entropy for the one-dimensional quantum harmonic…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
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…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…
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…
We present a numerical method to evaluate mutual information (MI) in nonlinear Gaussian noise channels by using denoising score matching (DSM) learning for estimating the score function of channel output. Via de Bruijn's identity, Fisher…
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…
New inequalities are proved for the variance of the Pitman estimators (minimum variance equivariant estimators) of \theta constructed from samples of fixed size from populations F(x-\theta). The inequalities are closely related to the…
We consider a general stochastic input-output dynamical system with output evolving in time as the solution to a functional coefficients, It\^{o}'s stochastic differential equation, excited by an input process. This general class of…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…
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.