ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2406.01094
24
0

Joint Learning of Linear Dynamical Systems under Smoothness Constraints

3 June 2024
Hemant Tyagi
ArXivPDFHTML
Abstract

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 mmm linear systems each of which resides on a node of a given undirected graph G=([m],E)G = ([m], \mathcal{E})G=([m],E). We assume that the system matrices are marginally stable, and satisfy a smoothness constraint w.r.t GGG -- akin to the quadratic variation of a signal on a graph. Given access to the states of the nodes over TTT 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 mmm increases, typically polynomially fast w.r.t mmm. The results hold under mild (i.e., T∼log⁡mT \sim \log mT∼logm), or sometimes, even no assumption on TTT (i.e. T≥2T \geq 2T≥2).

View on arXiv
Comments on this paper