Related papers: Inferring an optimal Fisher measure
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…
The eigenvalues and eigenvectors of the Fisher information matrix (FIM) can reveal the most and least sensitive directions of a system and it has wide application across science and engineering. We present a symplectic variant of the…
The integrating factor technique is widely used to solve numerically (in particular) the Schr\"odinger equation in the context of spectral methods. Here, we present an improvement of this method exploiting the freedom provided by the gauge…
This paper considers the problem of state tracking with observation control for a particular class of dynamical systems. The system state evolution is described by a discrete-time, finite-state Markov chain, while the measurement process is…
F-measures are popular performance metrics, particularly for tasks with imbalanced data sets. Algorithms for learning to maximize F-measures follow two approaches: the empirical utility maximization (EUM) approach learns a classifier having…
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…
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…
It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramer-Rao bound (CRB), a popular tool to lower bound the…
Studies about Quantum Information Theory continue actively in many research institutions. Very recently, pratical setups of large scale quantum computers are widely studied e.g. quantum repeaters, memories and processors. Entanglement…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state, and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for…
Discrete events alter how parameter influence propagates in hybrid systems. Prevailing Fisher information formulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the…
We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is…
We present a numerical method to evaluate mutual information (MI) in nonlinear Gaussian noise channels by using denoising score matching (DSM) learning for estimating the score function of channel output. Via de Bruijn's identity, Fisher…
In recent years forecasting activities have become a very important tool for designing and optimising large scale structure surveys. To predict the performance of such surveys, the Fisher matrix formalism is frequently used as a fast and…
Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We employ an IM-based technique to marginalize out the unknown…
In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square…
We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation.…
The Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a…