Time varying regression with hidden linear dynamics

2021/12/29 by Ali Jadbabaie, Jadbabaie, Ali, Horia Mania +5
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Statistics Theory (math.ST) #math.OC #math.ST #stat.ML #stat.TH

paper · pdf · doi:10.48550/arxiv.2112.14862

22 pages

arxiv created 2021/12/29 · arxiv updated 2022/01/03

Abstract

We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates. We offer a finite sample guarantee on the estimation error of our method and discuss certain advantages it has over Expectation-Maximization (EM), which is the main approach proposed by prior work.

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