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  • 51.
    Umenberger, Jack
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Learning convex bounds for linear quadratic control policy synthesis2018In: Neural Information Processing Systems 2018, 2018, Vol. 31Conference paper (Refereed)
    Abstract [en]

    Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a numbers of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of learning control policies for unknown linear dynamical systems so as to maximize a quadratic reward function. We present a method to optimize the expected value of the reward over the posterior distribution of the unknown system parameters, given data. The algorithm involves sequential convex programing, and enjoys reliable local convergence and robust stability guarantees. Numerical simulations and stabilization of a real-world inverted pendulum are used to demonstrate the approach, with strong performance and robustness properties observed in both.

  • 52.
    Umenberger, Jack
    et al.
    Univ Sydney, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW, Australia.
    Wågberg, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Manchester, Ian R.
    Univ Sydney, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW, Australia.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Maximum likelihood identification of stable linear dynamical systems2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 96, p. 280-292Article in journal (Refereed)
    Abstract [en]

    This paper concerns maximum likelihood identification of linear time invariant state space models, subject to model stability constraints. We combine Expectation Maximization (EM) and Lagrangian relaxation to build tight bounds on the likelihood that can be optimized over a convex parametrization of all stable linear models using semidefinite programming. In particular, we propose two new algorithms: EM with latent States & Lagrangian relaxation (EMSL), and EM with latent Disturbances & Lagrangian relaxation (EMDL). We show that EMSL provides tighter bounds on the likelihood when the effect of disturbances is more significant than the effect of measurement noise, and EMDL provides tighter bounds when the situation is reversed. We also show that EMDL gives the most broadly applicable formulation of EM for identification of models with singular disturbance covariance. The two new algorithms are validated with extensive numerical simulations.

  • 53. Umenberger, Jack
    et al.
    Wågberg, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Manchester, Ian R.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On Identification via EM with Latent Disturbances and Lagrangian Relaxation2015Conference paper (Refereed)
    Abstract [en]

    In the application of the Expectation Maximization (EM) algorithm to identification of dynamical systems, latent variables are typically taken as system states, for simplicity. In this work, we propose a different choice of latent variables, namely, system disturbances. Such a formulation is shown, under certain circumstances, to improve the fidelity of bounds on the likelihood, and circumvent difficulties related to intractable model transition densities. To access these benefits, we propose a Lagrangian relaxation of the challenging optimization problem that arises when formulating over latent disturbances, and fully develop the method for linear models.

  • 54.
    Vaicenavicius, Juozas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Widmann, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Andersson, Carl
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Lindsten, Fredrik
    Roll, Jacob
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Evaluating model calibration in classification2019In: 22nd International Conference on Artificial Intelligence and Statistics, 2019, p. 3459-3467Conference paper (Refereed)
  • 55.
    Valenzuela, Patricio E.
    et al.
    KTH Royal Inst Technol, Dept Automat Control, SE-10044 Stockholm, Sweden..
    Dahlin, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Rojas, Cristian R.
    KTH Royal Inst Technol, Dept Automat Control, SE-10044 Stockholm, Sweden..
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On robust input design for nonlinear dynamical models2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 77, p. 268-278Article in journal (Refereed)
    Abstract [en]

    We present a method for robust input design for nonlinear state-space models. The method optimizes a scalar cost function of the Fisher information matrix over a set of marginal distributions of stationary processes. By using elements from graph theory we characterize such a set. Since the true system is unknown, the resulting optimization problem takes the uncertainty on the true value of the parameters into account. In addition, the required estimates of the information matrix are computed using particle methods, and the resulting problem is convex in the decision variables. Numerical examples illustrate the proposed technique by identifying models using the expectation-maximization algorithm.

  • 56.
    Valenzuela, Patricio E.
    et al.
    KTH.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Rojas, Cristian R.
    KTH.
    On model order priors for Bayesian identification of SISO linear systems2019In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 92, no 7, p. 1645-1661Article in journal (Refereed)
    Abstract [en]

    A method for the identification of single input single output linear systems is presented. The method employs a Bayesian approach to compute the posterior distribution of the model parameters given the data-set. Since this distribution is often unavailable in closed form, a Metropolis Hastings algorithm is implemented to draw samples from it. To implement the sampler, the inclusion of prior information regarding the model order of the identified system is discussed. As one of the main contributions of this work, a prior over the Hankel singular values of the model is imposed. Numerical examples illustrate the method.

  • 57.
    Valenzuela, Patricio L.
    et al.
    KTH Royal Inst Technol, Sch Elect Engn, Dept Automat Control, SE-10044 Stockholm, Sweden.;KTH Royal Inst Technol, Sch Elect Engn, ACCESS Linnaeus Ctr, SE-10044 Stockholm, Sweden..
    Dahlin, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
    Rojas, Cristian R.
    KTH Royal Inst Technol, Sch Elect Engn, Dept Automat Control, SE-10044 Stockholm, Sweden.;KTH Royal Inst Technol, Sch Elect Engn, ACCESS Linnaeus Ctr, SE-10044 Stockholm, Sweden..
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Particle-based Gaussian process optimization for input design in nonlinear dynamical models2016In: 2016 IEEE 55th Conference On Decision And Control (CDC), New York: IEEE, 2016, p. 2085-2090Conference paper (Refereed)
    Abstract [en]

    We propose a novel approach to input design for identification of nonlinear state space models. The optimal input sequence is obtained by maximizing a scalar cost function of the Fisher information matrix. Since the Fisher information matrix is unavailable in closed form, it is estimated using particle methods. In addition, we make use of Gaussian process optimization to find the optimal input and to mitigate the problem of a large computational cost incurred by the particle method, as the method reduces the number of functional evaluations. Numerical examples are provided to illustrate the performance of the resulting algorithm.

  • 58.
    Wallert, John
    et al.
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Women's and Children's Health, Research group (Dept. of women´s and children´s health), Clinical Psychology in Healthcare.
    Pingel, Ronnie
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    Olsson, Erik
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Women's and Children's Health, Research group (Dept. of women´s and children´s health), Clinical Psychology in Healthcare.
    Madison, Guy
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Psychology.
    Hallqvist, Johan
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Public Health and Caring Sciences, Family Medicine and Preventive Medicine.
    Geale, Kirk
    Avdelningen för folkhälsa och klinisk medicin.
    Held, Claes
    Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Medicinska och farmaceutiska vetenskapsområdet, centrumbildningar mm, UCR-Uppsala Clinical Research Center.
    Derivation and validation of STOPSMOKE: An instrument built from Swedish population data for predicting smoking abstinence post myocardial infarctionManuscript (preprint) (Other academic)
  • 59. Wills, Adrian G.
    et al.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On the construction of probabilistic Newton-type algorithms2017In: Proc. 56th Conference on Decision and Control, Piscataway, NJ: IEEE, 2017, p. 6499-6504Conference paper (Refereed)
  • 60.
    Wågberg, Johan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Lindsten, Fredrik
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Bayesian nonparametric identification of piecewise affine ARX systems2015Conference paper (Refereed)
    Abstract [en]

    We introduce a Bayesian nonparametric approach to identification of piecewise affine ARX systems. The clustering properties of the Dirichlet process are used to construct a prior over the partition of the regressor space as well as the parameters of each local model. This enables us to probabilistically reason about and to identify the number of modes, the partition of the regressor space, and the linear dynamics of each local model from data. By appropriate choices of base measure and likelihood function, we give explicit expressions for how to perform both inference and prediction. Simulations and experiments on real data from a pick and place machine are used to illustrate the capabilities of the new approach.

  • 61.
    Wågberg, Johan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Zachariah, Dave
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Regularized parametric system identification:: a decision-theoretic formulation2018In: Proceedings of the American Control Conference (ACC), Milwaukee, WI, USA, June, 2018., IEEE, 2018Conference paper (Refereed)
    Abstract [en]

    Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian methods, has also gained attention. Methods based on this approach estimate the system impulse response with excellent small-sample properties. In several applications, however, it is desirable to obtain a compact representation of the system in the form of a parametric model. By viewing the identification of such models as a decision, we develop a decision-theoretic formulation of the parametric system identification problem that bridges the gap between the classical and regularized approaches above. Using the output-error model class as an illustration, we show that this decision-theoretic approach leads to a regularized method that is robust to small sample-sizes as well as overparameterization.

  • 62.
    Wågberg, Johan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Zachariah, Dave
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Prediction performance after learning in Gaussian process regression2016In: 25th European Research Network System Identification Workshop, 2016Conference paper (Refereed)
  • 63.
    Wågberg, Johan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Zachariah, Dave
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Prediction Performance After Learning in Gaussian Process Regression2017In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR , 2017, Vol. 54, p. 1264-1272Conference paper (Refereed)
    Abstract [en]

    This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the statistical model is learned from the data. We show that this omission leads to a systematic underestimation of the prediction errors. Starting from a generalization of the Cramér-Rao bound, we derive a more accurate MSE bound which provides a measure of uncertainty for prediction of Gaussian processes. The improved bound is easily computed and we illustrate it using synthetic and real data examples.

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