Related papers: Stochastic time-evolution, information geometry an…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the…
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…
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector. We address the question of how long the…
Mimicking the maximum likelihood estimator, we construct first order Cramer-Rao efficient and explicitly computable estimators for the scale parameter $\sigma^2$ in the model $Z_{i,n}=\sigma n^{-\beta}X_i+Y_i,i=1,\ldots,n,\beta>0$ with…
In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…
The Cramer-Rao product of the Fisher information and the variance of a probability density \rho(x), defined on a domain \Delta \in R^D, is found to have a minimum value reached by the density associated with the ground state of the harmonic…
The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
Recent studies found that many channels are affected by additive noise that is impulsive in nature and is best explained by heavy-tailed symmetric alpha-stable distributions. Dealing with impulsive noise environments comes with an added…
In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cram\'er-Rao inequality is…
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…
The paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field.…
We consider the problem of estimating an arbitrary dynamical parameter of an quantum open system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be…
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the…
This paper presents description of time evolution of averages of Markov process in wide range of noise intensity. Exact expression of time scale of average evolution has been obtained. It has been demonstrated numerically that for purely…
We analyzed the noncommutativity effects on the Fisher information (F_(r,p)) and Shannon entropies (S_(r,p)) of a harmonic oscillator immersed in a time-varying electric field in two and three dimensions. We find the exact solutions of the…
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…