Dealing with collinearity in large-scale linear system identification using Bayesian regularization

• URL: http://arxiv.org/abs/2203.13633v1
• Date: Fri, 25 Mar 2022 13:11:26 GMT
• Title: Dealing with collinearity in large-scale linear system identification using Bayesian regularization
• Authors: Wenqi Cao and Gianluigi Pillonetto
• Abstract summary: We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth exponential decay of the impulse responses. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses. It is based on a variation of Gibbs sampling which updates possibly overlapping blocks of the parameter space on the basis of the level of collinearity affecting the different inputs. Numerical experiments are included to test the goodness of the approach where hundreds of impulse responses form the system and inputs correlation may be very high.

Related papers

• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Weak Collocation Regression for Inferring Stochastic Dynamics with L\'{e}vy Noise [8.15076267771005]
  We propose a weak form of the Fokker-Planck (FP) equation for extracting dynamics with L'evy noise. Our approach can simultaneously distinguish mixed noise types, even in multi-dimensional problems.
  arXiv  Detail & Related papers  (2024-03-13T06:54:38Z)
• An information field theory approach to Bayesian state and parameter estimation in dynamical systems [0.0]
  This paper develops a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. We construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely.
  arXiv  Detail & Related papers  (2023-06-03T16:36:43Z)
• Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression [3.04585143845864]
  We consider estimation of networks consisting of several interconnected dynamic systems. We develop a strategy cast in a Bayesian regularization framework where any impulse response is seen as realization of a zero-mean Gaussian process. We design a novel Markov chain Monte Carlo scheme able to reconstruct the impulse responses posterior by efficiently dealing with collinearity.
  arXiv  Detail & Related papers  (2023-02-21T19:35:47Z)
• Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics [64.72260320446158]
  We propose a method for synthesising controllers for Markov jump linear systems. Our method is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS. We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.
  arXiv  Detail & Related papers  (2022-12-01T17:36:30Z)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• System identification using Bayesian neural networks with nonparametric noise models [0.0]
  We propose a nonparametric approach for system identification in discrete time nonlinear random dynamical systems. A Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated in simulated and real time series.
  arXiv  Detail & Related papers  (2021-04-25T09:49:50Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Feedback-induced instabilities and dynamics in the Jaynes-Cummings model [62.997667081978825]
  We investigate the coherence and steady-state properties of the Jaynes-Cummings model subjected to time-delayed coherent feedback. The introduced feedback qualitatively modifies the dynamical response and steady-state quantum properties of the system.
  arXiv  Detail & Related papers  (2020-06-20T10:07:01Z)
• Risk bounds when learning infinitely many response functions by ordinary linear regression [1.6114012813668934]
  Training data consist of a single independent random sample of the input variables drawn from a common distribution together with the associated responses. We provide convergence guarantees on the worst-case excess prediction risk by controlling the convergence rate of the excess risk uniformly in the response function. The collection of response functions, although potentially infinite, is supposed to have a finite Vapnik-Chervonenkis dimension.
  arXiv  Detail & Related papers  (2020-06-16T14:54:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.