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Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…

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…

Statistics Theory · Mathematics 2007-06-13 Alessandra Luati

Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this…

Machine Learning · Computer Science 2012-02-20 Quanquan Gu , Zhenhui Li , Jiawei Han

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…

Statistical Mechanics · Physics 2015-06-24 F. Pennini , A. Plastino , G. L. Ferri

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…

Quantum Physics · Physics 2018-05-09 Carlo Cafaro , Paul M. Alsing

The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…

Methodology · Statistics 2023-02-07 Maud Delattre , Estelle Kuhn

In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These…

Machine Learning · Statistics 2018-09-27 Huangjie Zheng , Jiangchao Yao , Ya Zhang , Ivor W. Tsang , Jia Wang

Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We…

Functional Analysis · Mathematics 2017-02-15 Patrick L. Combettes

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…

Statistical Mechanics · Physics 2009-11-13 Piotr Garbaczewski

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…

Machine Learning · Computer Science 2025-02-18 Gido M. van de Ven

The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can…

General Finance · Quantitative Finance 2022-03-24 Marcin Makowski , Edward W. Piotrowski , Piotr Frąckiewicz , Marek Szopa

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general…

Information Theory · Computer Science 2020-05-22 Leighton Pate Barnes , Wei-Ning Chen , Ayfer Ozgur

For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always…

Computation · Statistics 2015-11-13 Antonio Forcina

Using information theory, we propose an estimation method for traits parameters in a Darwinian evolution model for species with on trait or multiple traits. We use the Fisher's information to obtain the errors on the estimation for one…

Populations and Evolution · Quantitative Biology 2024-03-11 Eddy Kwessi

We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master…

Quantum Physics · Physics 2013-04-03 Søren Gammelmark , Klaus Mølmer

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…

Computation · Statistics 2021-04-16 Xuan Wu

A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…

Statistical Mechanics · Physics 2007-05-23 R. C. Venkatesan

The Fisher information matrix (FM) plays an important role in forecasts and inferences in many areas of physics. While giving fast parameter estimation with the Gaussian likelihood approximation in the parameter space, the FM can only give…

General Relativity and Quantum Cosmology · Physics 2022-06-22 Ziming Wang , Chang Liu , Junjie Zhao , Lijing Shao

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…

Statistics Theory · Mathematics 2024-03-05 Rémy Degenne , Timothée Mathieu

The Fisher information matrix (FIM) is a fundamental quantity to represent the characteristics of a stochastic model, including deep neural networks (DNNs). The present study reveals novel statistics of FIM that are universal among a wide…

Machine Learning · Statistics 2019-10-10 Ryo Karakida , Shotaro Akaho , Shun-ichi Amari