Related papers: Two Proofs of the Fisher Information Inequality vi…
We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of…
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.
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
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…
Machine-learning models contain information about the data they were trained on. This information leaks either through the model itself or through predictions made by the model. Consequently, when the training data contains sensitive…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
I present several new relations between mutual information (MI) and statistical estimation error for a system that can be regarded simultaneously as a communication channel and as an estimator of an input parameter. I first derive a…
We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states…
Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a…
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
In this note we consider inequalities involving the error function $\phi$. Our methodes give new proofs of some known inequalities of Komatsu, and of Szarek and Werner, and also produce two families of inequalities that give upper and lower…
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…
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,…
The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model…
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 apply the classical data processing inequality to quantum metrology to show that manipulating the classical information from a quantum measurement cannot aid in the estimation of parameters encoded in quantum states. We further derive a…
Privacy is under threat from artificial intelligence revolution fueled by unprecedented abundance of data. Differential privacy, an established candidate for privacy protection, is susceptible to adversarial attacks, acts conservatively,…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…