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Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, there is no notion of design optimality…

Statistics Theory · Mathematics 2019-12-04 Yi Lin , Ryan Martin , Min Yang

It is well known that a suggestive relation exists that links Schr\"odinger's equation (SE) to the information-optimizing principle based on Fisher's information measure (FIM). We explore here an approach that will allow one to infer the…

Statistics Theory · Mathematics 2015-05-27 S. P. Flego , A. Plastino , A. R. Plastino

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…

Information Theory · Computer Science 2018-05-30 Manuel Stein , Josef A. Nossek

The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…

Computation · Statistics 2014-05-08 Xumeng Cao

We derive upper bounds on the quantum Fisher information in interferometry with $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence of arbitrarily correlated Gaussian dephasing including independent and collective…

Quantum Physics · Physics 2014-03-06 Katarzyna Macieszczak

We consider the problem of estimating the direction of arrival of a signal embedded in $K$-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information…

Applications · Statistics 2015-10-28 Yuri Abramovich , Olivier Besson , Ben Johnson

This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of…

Statistics Theory · Mathematics 2026-04-02 Telmo Pérez-Izquierdo

Preconditioning with the quantum Fisher information matrix (QFIM) is a popular approach in quantum variational algorithms. Yet the QFIM is costly to obtain directly, usually requiring more state preparation than its classical counterpart:…

Quantum Physics · Physics 2026-04-09 Jianfeng Lu , Kecen Sha

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…

Quantum Physics · Physics 2025-05-16 Wojciech Górecki , Xi Lu , Chiara Macchiavello , Lorenzo Maccone

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…

Quantum Physics · Physics 2017-05-04 R. Yousefjani , S. Salimi , A. S. Khorashad

The Fisher information matrix (FIM) plays an essential role in statistics and machine learning as a Riemannian metric tensor or a component of the Hessian matrix of loss functions. Focusing on the FIM and its variants in deep neural…

Machine Learning · Statistics 2020-09-29 Ryo Karakida , Shotaro Akaho , Shun-ichi Amari

Motivated by the growing interest in quantum machine learning, in particular quantum neural networks (QNNs), we study how recently introduced evaluation metrics based on the Fisher information matrix (FIM) are effective for predicting their…

Machine Learning · Computer Science 2025-10-09 Lorenzo Pastori , Veronika Eyring , Mierk Schwabe

We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…

Machine Learning · Computer Science 2023-10-09 Paul M. Riechers

We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…

Quantum Physics · Physics 2026-05-22 Pedro B. Melo

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…

Statistics Theory · Mathematics 2015-07-28 Katarína Burclová , Andrej Pázman

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…

Machine Learning · Statistics 2022-10-07 Sinho Chewi , Patrik Gerber , Holden Lee , Chen Lu

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…

Quantum Physics · Physics 2012-11-21 B. M. Escher , L. Davidovich , N. Zagury , R. L. de Matos Filho

The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…

Numerical Analysis · Mathematics 2026-04-14 Kathrin Hellmuth , Christian Klingenberg , Qin Li

The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…

Computation · Statistics 2016-08-08 Lingyao Meng

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…

Quantum Physics · Physics 2017-08-02 Yu Chen , Haidong Yuan