相关论文: Fisher Information in Group-Type Models

We prove that in the 2d Ising Model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case, that is the critical exponents for the specific heat and…

We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning…

Fisher-information inequalities have recently been used as operational witnesses of nonclassical metrological behavior, but their physical meaning is often tied to a particular narrative, such as, segmented dynamics or discrete…

The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian…

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 study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism $H$ between the solutions of a linear ODE system having exponential dichotomy and a quasilinear…

We extend classical analytic tools for finite-state statistical models to allow zero probabilities. Using methods from algebraic statistics and information geometry, we develop a framework in which a smooth statistical model could hit the…

Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…

Precision measurements with quantum systems rely on our ability to trace the differences between experimental signals to variations in unknown physical parameters. In this Letter we derive the Fisher information and the ensuing Cramer-Rao…

A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…

This paper focusses on robust estimation of location and concentration parameters of the von Mises-Fisher distribution in the Bayesian framework. The von Mises-Fisher (or Langevin) distribution has played a central role in directional…

We prove that for a large class of quantum Fisher information, a quantum channel is sufficient for a family of quantum states, i.e., the input states can be recovered from the output, if and only if the quantum Fisher information is…

Postselected weak measurement has shown significant potential for detecting small physical effects due to its unique weak-value-amplification phenomenon. Previous works suggest that Heisenberg-limit precision can be attained using only the…

Kiefer and Wolfowitz [Z. Wahrsch. Verw. Gebiete 34 (1976) 73--85] showed that if $F$ is a strictly curved concave distribution function (corresponding to a strictly monotone density $f$), then the Maximum Likelihood Estimator $\hat{F}_n$,…

Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part…

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states…

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on…

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…

Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…