Related papers: Fisher Information and Dynamical Sampling I
Beyond the linear regime of structure formation, part of cosmological information encoded in galaxy clustering becomes inaccessible to the usual power spectrum. "Sufficient statistics", A*, were introduced recently to recapture the lost,…
In recent years, in quantum information theory, there has been a remarkable development in the general theoretical framework for studying symmetry in dynamics. This development, called resource theory of asymmetry, is expected to have a…
Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the…
We demonstrate that the algorithmic information content of a system is deeply connected to its potential dynamics, thus affording an avenue for moving systems in the information-theoretic space and controlling them in the phase space. To…
The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale…
In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…
A steadily growing computational power is employed to perform molecular dynamics simulations of biological macromolecules, which represents at the same time an immense opportunity and a formidable challenge. In fact, large amounts of data…
The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model…
Clinical prediction models enable healthcare professionals to estimate individual outcomes using patient characteristics. Current sample size guidelines for developing or updating models with continuous outcomes aim to minimise overfitting…
We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…
We derive general expressions for the multi-tracer Fisher matrix, both assuming that the cross-spectra are constrained by the auto-spectra, and also allowing for independent degrees of freedom in the cross-spectra. We show that, just like…
We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…
We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
Computational intelligence is broadly defined as biologically-inspired computing. Usually, inspiration is drawn from neural systems. This article shows how to analyze neural systems using information theory to obtain constraints that help…
In the realm of deep learning, the Fisher information matrix (FIM) gives novel insights and useful tools to characterize the loss landscape, perform second-order optimization, and build geometric learning theories. The exact FIM is either…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum information} number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else…