Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual Reviews in Contro

NeuroPrime: a Pythonic framework for the priming of brain states in self-regulation protocols

Due to the recent pandemic and a general boom in technology, we are facing more and more threats of isolation, depression, fear, overload of information, between others. In turn, these affect our Self, psychologically and physically. Therefore, new tools are required to assist the regulation of this unregulated Self to a more personalized, optimal and healthy Self. As such, we developed a Pythonic open-source humancomputer framework for assisted priming of subjects to “optimally” self-regulate their Neurofeedback (NF) with external stimulation, like guided mindfulness. For this, we did a three-part study in which: 1) we defined the foundations of the framework and its design for priming subjects to self-regulate their NF, 2) developed an open-source version of the framework in Python, NeuroPrime, for utility, expandability and reusability, and 3) we tested the framework in neurofeedback priming versus no-priming conditions. NeuroPrime is a research toolbox developed for the simple and fast integration of advanced online closed-loop applications. More specifically, it was validated and tuned for the research of priming brain states in an EEG neurofeedback setup. In this paper, we will explain the key aspects of the priming framework, the NeuroPrime software developed, the design decisions and demonstrate/validate the use of our toolbox by presenting use cases of priming brain states during a neurofeedback setup.MIT -Massachusetts Institute of Technology(PD/BD/114033/2015

Stochastic gradient descent on Riemannian manifolds

Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the gradient descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and is illustrated here by four examples. In particular a novel gossip algorithm on the set of covariance matrices is derived and tested numerically.Comment: A slightly shorter version has been published in IEEE Transactions Automatic Contro