The natural gradient learning method is known to have ideal performances for on-line training of multilayer perceptrons. It avoids plateaus which give rise to slow convergence of the backpropagation method. It is Fisher eecient whereas the conventional method is not. However, for implementing the method, it is necessary to calculate the Fisher information matrix and its inverse, which is practi...

The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simu...

The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in ...

Fisher information has been used to analyze the accuracy of neural population coding. This works well when the Fisher information does not degenerate, but when two stimuli are presented to a population of neurons, a singular structure emerges by their mutual interactions. In this case, the Fisher information matrix degenerates, and the regularity condition ensuring the Cramér-Rao paradigm of st...

In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...

The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact calculation scales with the third power of the number of data points N and is therefore computationally prohibitive for state-of-the-art surveys. Applicable to a very...

We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix. The assumptions that we make limit our analysis to order parameters representable as a negative derivative of thermodynamic potential over some thermodynamic variable. Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of...

We discuss the local asymptotic behavior of the likelihood function associated with all the four characterizing parameters (α,β ,δ ,μ) of the Meixner Lévy process under high-frequency sampling scheme. We derive the optimal rate of convergence for each parameter and the Fisher information matrix in a closed form. The skewness parameter β exhibits a slower rate alone, relative to the other three ...

We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the inverse of the Fisher information matrix. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm is of order O(n 2) while the complexity of conventional algorit...

This paper examines the problem of relative attitude observability for formations of three, four and five vehicle formations. The analysis is rooted in within the principles of maximum likelihood estimation insomuch as the metric for observability is the resulting Fisher information matrix for the small attitude errors. For formations of three and four vehicles it is shown that the relative att...