Related papers: The Fisher score on the closed simplex
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
Fluid flows containing dilute or dense suspensions of thin fibers are widespread in biological and industrial processes. To describe the motion of a thin immersed fiber, or to describe the forces acting on it, it is convenient to work with…
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…
Algebraic statistics is a recently evolving field, where one would treat statistical models as algebraic objects and thereby use tools from computational commutative algebra and algebraic geometry in the analysis and computation of…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
Fisher forecasts are a common tool in cosmology with applications ranging from survey planning to the development of new cosmological probes. While frequently adopted, they are subject to numerical instabilities that need to be carefully…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
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…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
We consider evolutionary Stokes system, coupled with the so-called dynamic slip boundary condition, in the simple geometry of a $d$-dimensional half-space. Using the standard technique of the Fourier transform in tangential directions, we…
The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local…
In this investigation we revisit the concept of "effective free surfaces" arising in the solution of the time-averaged fluid dynamics equations in the presence of free boundaries. This work is motivated by applications of the optimization…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
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…
We develop an information-theoretic framework for bounding the supremum of stochastic processes, offering a simpler and sharper alternative to classical chaining and slicing arguments for generalization bounds. The key idea is a lifting…