Results 41 to 50 of about 944,515 (124)

The Fisher metric as a metric on the cotangent bundle

, 2023
The Fisher metric on a manifold of probability distributions is usually treated as a metric on the tangent bundle. In this paper, we focus on the metric on the cotangent bundle induced from the Fisher metric with calling it the Fisher co-metric.
Nagaoka, Hiroshi
core  

Curvature-Corrected Rotary Position Embeddings: An Entropy-Invariant Temperature for Mitigating Numerical-Rank Collapse in Long-Context Attention

Mathematics
As large language models process ever longer contexts, the positional encoding—most commonly rotary position embeddings (RoPEs)—must remain numerically trustworthy.
Joseph Tafataona Mtetwa, Kingsley A. Ogudo, Sameerchand Pudaruth   +2 more
doaj   +1 more source

On Closed-Form Expressions for the Fisher-Rao Distance [PDF]

The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to supervised and
Meneghetti, Fábio C. C., Pinele, Julianna, Miyamoto, Henrique K., Costa, Sueli I. R.   +3 more
core   +1 more source

Approximation to the Fisher–Rao metric for the focus of expansion [PDF]

, 2008
The Fisher–Rao metric for the focus of expansion is approximated, under the assumption that the focus is estimated from correspondences between two images taken by a translating camera.
Maybank, Stephen J.
core   +1 more source

Optimum Waveform Selection for Target State Estimation in the Joint Radar-Communication System

IEEE Open Journal of Signal Processing
The widespread usage of the Radio Frequency (RF) spectrum for wireless and mobile communication systems generated a significant spectrum scarcity. The Joint Radar-Communication System (JRCS) provides a framework to simultaneously utilize the allocated ...
Ashoka Chakravarthi Mahipathi, Bethi Pardha Pardhasaradhi, Srinath Gunnery, Pathipati Srihari, John D'Souza, Paramananda Jena   +5 more
doaj   +1 more source

Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric [PDF]

, 2016
34 pages, comments welcomeWe study a second-order variational problem on the group of diffeomorphisms of the interval [0, 1] endowed with a right-invariant Sobolev metric of order 2, which consists in the minimization of the acceleration.
Tahraoui, Rabah, Vialard, François-Xavier   +1 more
core   +2 more sources

A métrica de Fisher-Rao : abordagem geométrica em probabilidade e estatística [PDF]

, 2023
Dissertação (mestrado) — Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2023.Nesta dissertação, veremos como a matriz de informação de Fisher dá origem a uma métrica riemanniana em modelos estatísticos paramétricos ...
Leite, Saulo Henrique Furtado
core  

Estimating multiplicity of infection, allele frequencies, and prevalences accounting for incomplete data.

PLoS ONE
BackgroundMolecular surveillance of infectious diseases allows the monitoring of pathogens beyond the granularity of traditional epidemiological approaches and is well-established for some of the most relevant infectious diseases such as malaria.
Meraj Hashemi, Kristan A Schneider
doaj   +1 more source

Shape Analysis Using the Fisher-Rao Riemannian Metric: Unifying Shape Representation and Deformation

, 2008
— We show that the Fisher-Rao Riemannian metric is a natural, intrinsic tool for computing shape geodesics. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically ...
Adrian Peter
core  

The Fisher-Rao geometry of CES distributions

International audienceWhen dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric.
Renaux, Alexandre, Breloy, Arnaud, Ginolhac, Guillaume, Collas, Antoine, Bouchard, Florent   +4 more
core   +1 more source