Related papers: Fisher Information Matrix of General Stable Distri…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011), and a method…
Let ${\Gamma}_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let ${ Z}_n$ be the $p\times q$ upper-left submatrix of ${\Gamma}_n$ and ${G}_n$ be a $p\times q$ matrix whose $pq$ entries are independent standard normals, where $p$ and…
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is…
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles…
Evolving feature densities across batches of training data bias cross-validation, making model selection and assessment unreliable (\cite{sugiyama2012machine}). This work takes a distributed density estimation angle to the training setting…
This paper considers the three-parameter exponentiated Weibull family under type II censoring. It first graphically illustrates the shape property of the hazard function. Then, it proposes a simple algorithm for computing the maximum…
This study presents the Fisher information for the position-dependent mass Schr\"odinger equation with hyperbolical potential {$V(x)=-V_0{\rm csch}^2(ax)$}. The analysis of the quantum-mechanical probability for the ground and exited states…
Consider two forms of sampling from a population: (i) drawing $s$ samples of $n$ elements with replacement and (ii) drawing a single sample of $ns$ elements. In this paper, under the setting where the descending order population frequency…
In this brief paper we revisit the Fisher information content of cosmological power spectra or two-point functions of Gaussian fields in order to comment on the assumption of Gaussian estimators and the use of parameter-dependent covariance…
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the…
The efficient sensing of weak environmental perturbations via special degeneracies called exceptional points in non-Hermitian systems has gained enormous traction in the last few decades. However, in contrast to the extensive literature on…
In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher…
We consider a certain infinite product of random $2 \times 2$ matrices appearing in the solution of some $1$ and $1+1$ dimensional disordered models in statistical mechanics, which depends on a parameter $\varepsilon>0$ and on a real random…
Morozova and Chentsov (Morozova and Chentsov 90) studied Riemannian metrics on the set of probability measures. They showed that, up to a constant factor, the Fisher information is the only Riemannian metric which is monotone under…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…
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…
In this paper, we propose generalizations of the de Bruijn's identities based on extensions of the Shannon entropy, Fisher information and their associated divergences or relative measures. The foundation of these generalizations are the…
We study the properties of optical pulse in cubic-quintic nonlinear media using information theoretic approach. The system can support regular (sharp top) and flat top pulse depending on the type of quintic interaction and the frequency of…