相关论文: Bounds for Fisher information and its production u…
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…
Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…
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 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…
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…
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 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…
The problem how to approximately determine the absolute value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric…
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…
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…
We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated…
We establish a variant of the log-Sobolev and transport-information inequalities for mixture distributions. If a probability measure $\pi$ can be decomposed into components that individually satisfy such inequalities, then any measure $\mu$…
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…
Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…
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 importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate…
Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…
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…
We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…
We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…