• Corpus ID: 245634516

Time Varying Regression with Hidden Linear Dynamics

  title={Time Varying Regression with Hidden Linear Dynamics},
  author={Horia Mania and Ali Jadbabaie and Devavrat Shah and Suvrit Sra},
  booktitle={Conference on Learning for Dynamics \& Control},
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… 

Can Direct Latent Model Learning Solve Linear Quadratic Gaussian Control?

This work focuses on an intu-itive cost-driven state representation learning method for solving Linear Quadratic Gaussian (LQG) control, one of the most fundamental partially observable control problems.



Identification of linear parameter varying models

  • Bassam BamiehL. Giarré
  • Mathematics
    Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)
  • 1999
We consider the problem of identifying discrete-time linear parameter varying models of nonlinear or time-varying systems. We assume that inputs, outputs and the scheduling parameters are measured,


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This work considers parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models, and proposes an information criterion that can consistently select the true set of significant predictors.

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It is demonstrated that prefiltered least squares yields the first algorithm that provably estimates the parameters of partially-observed linear systems that attains rates which do not not incur a worst-case dependence on the rate at which these dependencies decay.

Gradient Descent Learns Linear Dynamical Systems

We prove that gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy

Time-Varying Parameter Vector Autoregressions: Specification, Estimation, and an Application

Time-varying parameter vector autoregressions (TVP-VARs) have become a popular tool to study the dynamics of macroeconomic time series. In this article, we discuss the specification and estimation of

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This work proposes an algorithm to actively estimate the parameters of a linear dynamical system given complete control over the system's input and shows a finite time bound quantifying the estimation rate this algorithm attains and proves matching upper and lower bounds which guarantee its asymptotic optimality.

Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification

It is proved that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory, and generalizes the technique to provide bounds for a more general class of linear response time-series.

Learning Linear Dynamical Systems via Spectral Filtering

A polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning, based on a novel filtering technique, which may be of independent interest.