A new kernel-based approach for linear system identification

This paper describes a new kernel-based approach for linear system identification of stable systems. We model the impulse response as the realization of a Gaussian process whose statistics, differently from previously adopted priors, include information not only on smoothness but also on BIBO-stability. The associated autocovariance defines what we call a stable spline kernel. The corresponding minimum variance estimate belongs to a reproducing kernel Hilbert space which is spectrally characterized. Compared to parametric identification techniques, the impulse response of the system is searched for within an infinite-dimensional space, dense in the space of continuous functions. Overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization. The proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two-step procedure that projects the nonparametric estimate onto the space of nominal models. The continuous-time derivation immediately extends to the discrete-time case. On several continuous- and discrete-time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques.     

Motion planning using adaptive random walks

We propose a novel single-shot motion-planning algorithm based on adaptive random walks. The proposed algorithm turns out to be simple to implement, and the solution it produces can be easily and efficiently optimized. Furthermore, the algorithm can incorporate adaptive components, so the developer is not required to specify all the parameters of the random distributions involved, and the algorithm itself can adapt to the environment it is moving in. Proofs of the theoretical soundness of the algorithm are provided, as well as implementation details. Numerical comparisons with well-known algorithms illustrate its effectiveness.     

Reconstructing insulin secretion rate after a glucose stimulus byan improved stochastic deconvolution method

Reconstructing insulin secretion rate (ISR) after a glucose stimulus by deconvolution is difficult because of its biphasic pattern, i.e., a rapid secretion peak is followed by a slower release. Here, we refine a recently proposed stochastic deconvolution method by modeling ISR as the multiple integration of a white noise process with time-varying statistics. The unknown parameters are estimated from the data by employing a maximum likelihood criterion. A fast computational scheme implementing the method is presented. Monte Carlo simulation results are developed which numerically show a more reliable ISR profile reconstructed by the new method.     

Optimal smoothing of non-linear dynamic systems via Monte Carlo Markov chains

We consider the smoothing problem of estimating a sequence of state vectors given a nonlinear state space model with additive white Gaussian noise, and measurements of the system output. The system output may also be nonlinearly related to the system state. Often, obtaining the minimum variance state estimates conditioned on output data is not analytically intractable. To tackle this difficulty, a Markov chain Monte Carlo technique is presented. The proposal density for this method efficiently draws samples from the Laplace approximation of the posterior distribution of the state sequence given the measurement sequence. This proposal density is combined with the Metropolis-Hastings algorithm to generate realizations of the state sequence that converges to the proper posterior distribution. The minimum variance estimate and confidence intervals are approximated using these realizations. Simulations of a fed-batch bioreactor model are used to demonstrate that the proposed method can obtain significantly better estimates than the iterated Kalman-Bucy smoother.     

Prediction error identification of linear systems: A nonparametric Gaussian regression approach

A novel Bayesian paradigm for the identification of output error models has recently been proposed in which, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, such a nonparametric approach is applied to the design of optimal predictors and discrete-time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of Gaussian processes. The proposed scheme describes the predictor impulse responses as the convolution of an infinite-dimensional response with a low-dimensional parametric response that captures possible high-frequency dynamics. Overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization. Numerical experiments, with data generated by ARMAX and infinite-dimensional models, show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses.     

Boosting as a kernel-based method

Machine Learning - Boosting combines weak (biased) learners to obtain effective learning algorithms for classification and prediction. In this paper, we show a connection between boosting and...     

Consistent identification of Wiener systems: A machine learning viewpoint

Wiener system identification has been recently performed by adopting a Bayesian semiparametric approach. In this framework, the linear system entering the first block is given a finite-dimensional parametrization, while nonparametric Gaussian regression is used to estimate the static nonlinearity in the second block. In this paper, we study the asymptotic behavior of this estimator when the number of noisy output samples tends to infinity without assuming the correctness of the Bayesian prior models. For this purpose, we interpret Wiener identification under a machine learning perspective. This allows us to extend recent results on function estimation in reproducing kernel Hilbert spaces to derive a condition guaranteeing the statistical consistency of the identification procedure. We also discuss how the violation of such a condition can lead to useless estimates of the Wiener structure.     

A new dynamic index of insulin sensitivity

Insulin sensitivity is a crucial parameter of glucose metabolism. The standard measures of insulin sensitivity obtained by an euglycaemic hyperinsulinaemic clamp, S/sub I/(clamp), or by the minimal model (MM), S/sub I/, do not account for the dynamics of insulin action, i.e., how fast or slow insulin action reaches its plateau value. This is an important physiological information. In this paper we formally define a new insulin sensitivity index which also incorporates information on the dynamics of insulin action, S/sub I//sup D/, show its properties, and exemplify how it can be measured both with the clamp and the MM method. Then, by resorting to real and synthetic data, we show both in IVGTT MM and clamp studies why this new index S/sub I//sup D/ offers, in comparison with S/sub I/, a more comprehensive picture of the control of insulin on glucose.