Related papers: Information Geometry of Sensor Configuration
A statistical framework is introduced for a broad class of problems involving synchronization or registration of data across a sensor network in the presence of noise. This framework enables an estimation-theoretic approach to the design…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new…
We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to…
The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…
In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To…
We consider estimating the magnitude of a monochromatic AC signal that couples to a two-level sensor. For any detection protocol, the precision achieved depends on the signal's frequency and can be quantified by the quantum Fisher…
Relativistic quantum metrology studies the maximal achievable precision for estimating a physical quantity when both quantum and relativistic effects are taken into account. We study the relativistic quantum metrology of temperature in…
Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher…
The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source-detector pair, which creates the issue of…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
The expected decrease in system inertia and frequency stability motivates the development and maintenance of dynamic system models by Transmission System Operators. However, some dynamic model parameters can be unavailable due to market…
A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behavior. The classical approach is to investigate how individual neurons encode the stimuli and how their tuning…