Dynamic angular synchronization under smoothness constraints

Araya, Ernesto; Cucuringu, Mihai; Tyagi, Hemant

Type de document :

Pré-publication ou Document de travail

DOI :

10.48550/arXiv.2406.04071

Titre :

Dynamic angular synchronization under smoothness constraints

Auteur(s) :

Araya, Ernesto [Auteur]
Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München [LMU]
Cucuringu, Mihai [Auteur]
Tyagi, Hemant [Auteur]
MOdel for Data Analysis and Learning [MODAL]

Date de publication :

2024

Mot(s)-clé(s) en anglais :

Machine Learning (stat.ML)
Machine Learning (cs.LG)
Statistics Theory (math.ST)

Discipline(s) HAL :

Statistiques [stat]

Résumé en anglais : [en]

Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the classical angular synchronization problem consists of recovering unknown angles $θ_1^*,\dots,θ_n^*$ from a collection of noisy pairwise measurements ...
Lire la suite >Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the classical angular synchronization problem consists of recovering unknown angles $θ_1^*,\dots,θ_n^*$ from a collection of noisy pairwise measurements of the form $(θ_i^* - θ_j^*) \mod 2π$, for all $\{i,j\} \in \mathcal{E}$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from pairwise comparisons. In this paper, we consider a dynamic version of this problem where the angles, and also the measurement graphs evolve over $T$ time points. Assuming a smoothness condition on the evolution of the latent angles, we derive three algorithms for joint estimation of the angles over all time points. Moreover, for one of the algorithms, we establish non-asymptotic recovery guarantees for the mean-squared error (MSE) under different statistical models. In particular, we show that the MSE converges to zero as $T$ increases under milder conditions than in the static setting. This includes the setting where the measurement graphs are highly sparse and disconnected, and also when the measurement noise is large and can potentially increase with $T$. We complement our theoretical results with experiments on synthetic data.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

document
Accès libre
Accéder au document

2406.04071v1.pdf
Accès libre
Accéder au document

Dynamic angular synchronization under ... BibTeX CSV Excel RIS

Fichiers

Dynamic angular synchronization under ...

BibTeX

CSV

Excel

RIS