Related papers: Pearson information-based lower bound on Fisher in…
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…
The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved…
We study the optimality conditions of information transfer in systems with memory in the low signal-to-noise ratio regime of vanishing input amplitude. We find that the optimal mutual information is represented by a maximum-variance of the…
We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable…
When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been…
The Slepian-Bangs formula provides a very convenient way to compute the Fisher information matrix (FIM) for Gaussian distributed data. The aim of this letter is to extend it to a larger family of distributions, namely elliptically contoured…
Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism.…
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…
This paper establishes the privacy-preserving Cram\'er-Rao (CR) lower bound theory, characterizing the fundamental limit of identification accuracy under privacy constraint. An identifiability criterion under privacy constraint is derived…
Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore…
Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have…
We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
Advanced super-resolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to Cramer-Rao bound (CRB) has proved to be a powerful and…
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…
We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized $q$-Gaussian…