Related papers: Fisher information as a performance metric for loc…
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum…
The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005)]. An estimation theory of low-noise…
Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials…
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The…
For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting…
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can…
A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…
We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for…
The optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the…
Complex frequency excitations, oscillating signals whose amplitude decreases exponentially in time, have recently been demonstrated to significantly increase the effective quality factor of mechanical resonators. In this work, we…
It is a widely accepted fact that the computational capability of recurrent neural networks is maximized on the so-called "edge of criticality". Once the network operates in this configuration, it performs efficiently on a specific…
This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymptotic formulas for the mean square errors of the filtering…
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive for problems with highly…