Related papers: Pearson information-based lower bound on Fisher in…
The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap…
We consider non-linear regression models corrupted by generic noise when the regression functions form a non-linear subspace of L^2, relevant in non-linear PDE inverse problems and data assimilation. We show that when the score of the model…
In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task…
This paper presents state estimation and stochastic optimal control gathered in one global optimization problem generating dual effect i.e. the control can improve the future estimation. As the optimal policy is impossible to compute, a…
We study a scenario where a group of agents, each with multiple heterogeneous sensors are collecting measurements of a vehicle and the measurements are transmitted over a communication channel to a centralized node for processing. The…
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles…
The Fisher Information Matrix formalism is extended to cases where the data is divided into two parts (X,Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary…
The eigenvalues and eigenvectors of the Fisher information matrix (FIM) can reveal the most and least sensitive directions of a system and it has wide application across science and engineering. We present a symplectic variant of the…
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…
The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cram\'{e}r-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…
We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…
The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…
The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…
In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…
Quantifying the influence of infinitesimal changes in training data on model performance is crucial for understanding and improving machine learning models. In this work, we reformulate this problem as a weighted empirical risk minimization…
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…