Titre :

Joint Learning of Linear Dynamical Systems under Smoothness Constraints

Auteur(s) :

Tyagi, Hemant [Auteur]
MOdel for Data Analysis and Learning [MODAL]

Date de publication :

2024

Mot(s)-clé(s) en anglais :

Optimization and Control (math.OC)
Systems and Control (eess.SY)
Statistics Theory (math.ST)
Machine Learning (stat.ML)

Discipline(s) HAL :

Statistiques [stat]

Résumé en anglais : [en]

We consider the problem of joint learning of multiple linear dynamical systems. This has received significant attention recently under different types of assumptions on the model parameters. The setting we consider involves ...
Lire la suite >We consider the problem of joint learning of multiple linear dynamical systems. This has received significant attention recently under different types of assumptions on the model parameters. The setting we consider involves a collection of $m$ linear systems each of which resides on a node of a given undirected graph $G = ([m], \mathcal{E})$. We assume that the system matrices are marginally stable, and satisfy a smoothness constraint w.r.t $G$ -- akin to the quadratic variation of a signal on a graph. Given access to the states of the nodes over $T$ time points, we then propose two estimators for joint estimation of the system matrices, along with non-asymptotic error bounds on the mean-squared error (MSE). In particular, we show conditions under which the MSE converges to zero as $m$ increases, typically polynomially fast w.r.t $m$. The results hold under mild (i.e., $T \sim \log m$), or sometimes, even no assumption on $T$ (i.e. $T \geq 2$).Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL