no code implementations • 2 Oct 2024 • Mauro Bisiacco, Gianluigi Pillonetto

Motivated by this line of research, we investigate under this constraint all possible kernel expansions of the Gaussian kernel, one of the most widely used models in machine learning.

no code implementations • 25 Sep 2024 • Riccardo Alessandro Grimaldi, Giacomo Baggio, Ruggero Carli, Gianluigi Pillonetto

This paper investigates the existence of a separation principle between model identification and control design in the context of model predictive control.

no code implementations • 4 Oct 2023 • Alberto Giaretta, Mauro Bisiacco, Gianluigi Pillonetto

This includes the important exploration-exploitation problems where e. g. a set of agents/robots has to monitor an environment to reconstruct a sensorial field and their movements rules are continuously updated on the basis of the acquired knowledge on the field and/or the surrounding environment.

no code implementations • 2 May 2023 • Mauro Bisiacco, Gianluigi Pillonetto

Working in continuous-time, it is the purpose of this note to prove that the same result holds also for Mercer kernels.

no code implementations • 1 May 2023 • Mauro Bisiacco, Gianluigi Pillonetto

Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces where all the evaluation functionals are linear and bounded.

no code implementations • 21 Feb 2023 • Wenqi Cao, Gianluigi Pillonetto

Many problems arising in control require the determination of a mathematical model of the application.

no code implementations • 30 Jan 2023 • Gianluigi Pillonetto, Aleksandr Aravkin, Daniel Gedon, Lennart Ljung, Antônio H. Ribeiro, Thomas B. Schön

For this reason, we provide a survey of deep learning from a system identification perspective.

no code implementations • 25 Mar 2022 • Wenqi Cao, Gianluigi Pillonetto

We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs.

no code implementations • 12 Sep 2021 • Mauro Bisiacco, Gianluigi Pillonetto

It is only apparently confined to the linear setting and allows also to study an important set of nonlinear models.

no code implementations • 2 Sep 2021 • Mauro Bisiacco, Gianluigi Pillonetto

In this paper we show that the Australian model can be generalized and given a rigorous mathematical analysis, casting strategies of the type short-term pain for collective gain in the context of sliding-mode control, an important branch of nonlinear control theory.

no code implementations • 6 May 2020 • Mauro Bisiacco, Gianluigi Pillonetto

Overall, our new results provide novel mathematical foundations of stable RKHSs with impact on stability tests, impulse responses modeling and computational efficiency of regularized schemes for linear system identification.

no code implementations • 5 Sep 2019 • Mauro Bisiacco, Gianluigi Pillonetto

Many of them model unknown impulse responses exploiting the so called Reproducing Kernel Hilbert spaces (RKHSs) that enjoy the notable property of being in one-to-one correspondence with the class of positive semidefinite kernels.

no code implementations • 20 May 2019 • Alberto Dalla Libera, Ruggero Carli, Gianluigi Pillonetto

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps.

no code implementations • 7 Mar 2018 • Jonathan Jonker, Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto, Sarah Webster

We therefore suggest that the proposed approach be the {\it default choice} for estimating state space models outside of the Gaussian context, regardless of whether the error covariances are singular or not.

no code implementations • 8 Jun 2017 • Giulio Bottegal, Gianluigi Pillonetto

Generalized cross validation (GCV) is one of the most important approaches used to estimate parameters in the context of inverse problems and regularization techniques.

no code implementations • 3 May 2017 • Marco Todescato, Andrea Carron, Ruggero Carli, Gianluigi Pillonetto, Luca Schenato

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data.

no code implementations • 29 Dec 2016 • Gianluigi Pillonetto

One reason is that the RKHSs usually employed in machine learning do not embed the information available on dynamic systems, e. g. BIBO stability.

no code implementations • 3 Oct 2016 • Giulio Bottegal, Håkan Hjalmarsson, Gianluigi Pillonetto

In this paper we introduce a novel method for linear system identification with quantized output data.

no code implementations • 8 Aug 2016 • Aleksandr Y. Aravkin, Giulio Bottegal, Gianluigi Pillonetto

We show that boosting with this learner is equivalent to estimation with a special {\it boosting kernel} that depends on $K$, as well as on the regression matrix, noise variance, and hyperparameters.

no code implementations • 17 Jan 2016 • Diego Romeres, Giulia Prando, Gianluigi Pillonetto, Alessandro Chiuso

We consider an on-line system identification setting, in which new data become available at given time steps.

no code implementations • 12 Aug 2015 • Giulia Prando, Gianluigi Pillonetto, Alessandro Chiuso

In this paper, adopting Maximum Entropy arguments, we derive a new $\ell_2$ penalty deriving from a vector-valued kernel; to do so we exploit the structure of the Hankel matrix, thus controlling at the same time complexity, measured by the McMillan degree, stability and smoothness of the identified models.

no code implementations • 2 Jul 2015 • Gianluigi Pillonetto, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, Lennart Ljung

In this paper, a comparative study of estimators based on these different types of regularizers is reported.

no code implementations • 2 Jul 2015 • Diego Romeres, Gianluigi Pillonetto, Alessandro Chiuso

Unluckily, the stability of the predictors does not guarantee the stability of the impulse response of the system.

no code implementations • 26 Apr 2015 • Giulio Bottegal, Gianluigi Pillonetto, Håkan Hjalmarsson

Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.

no code implementations • 21 Nov 2014 • Giulio Bottegal, Aleksandr Y. Aravkin, Håkan Hjalmarsson, Gianluigi Pillonetto

In this paper, we introduce a novel method to robustify kernel-based system identification methods.

no code implementations • 29 Sep 2014 • Giulia Prando, Alessandro Chiuso, Gianluigi Pillonetto

Recent developments in linear system identification have proposed the use of non-parameteric methods, relying on regularization strategies, to handle the so-called bias/variance trade-off.

no code implementations • 22 Jul 2014 • Andrea Carron, Marco Todescato, Ruggero Carli, Luca Schenato, Gianluigi Pillonetto

We consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function.

no code implementations • 21 Dec 2013 • Giulio Bottegal, Aleksandr Y. Aravkin, Hakan Hjalmarsson, Gianluigi Pillonetto

In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification.

1 code implementation • 30 Sep 2013 • Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto

This paper extends linear system identification to a wide class of nonsmooth stable spline estimators, where regularization functionals and data misfits can be selected from a rich set of piecewise linear-quadratic (PLQ) penalties.

no code implementations • 22 Jan 2013 • Aleksandr Y. Aravkin, Bradley M. Bell, James V. Burke, Gianluigi Pillonetto

Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS).

no code implementations • 19 Jan 2013 • Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto

We introduce a class of quadratic support (QS) functions, many of which play a crucial role in a variety of applications, including machine learning, robust statistical inference, sparsity promotion, and Kalman smoothing.

no code implementations • NeurIPS 2010 • Alessandro Chiuso, Gianluigi Pillonetto

We introduce a new Bayesian nonparametric approach to identification of sparse dynamic linear systems.

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