18 juillet 2018

Catégorie : Journée d étude

Second workshop on gaussian processes at Saint-Étienne

(From 9th to 11th of October 2018)

More information on http://tugaut.perso.math.cnrs.fr/workshop02.html

Among many models, the Gaussian ones play a particular role. The central limit theorem for a sequence of real random variables leads naturally to consider Gaussian models. These also are fundamental in basic statistics like for the application of the chi2-test of adequation (with estimation of the parameters). After several decades of intense research, they appear to be central in many other contexts.

One of its significant appearances is through the Brownian motion (or its

derivative'' the white noise). In stock exchange, in fluid mechanic or in neuroscience, we are able to explain the small local perturbations which appear to behave quasi-randomly with the Brownian motion.

However, it would be extremely reductive to see the Gaussian model only through this point of view. Indeed, theoretically these models have become more and more sophisticated and well understood. Moreover, they have been considerably extended to a larger framework (computer vision, big data, machine learning...).

The first idea of Gaussian models that we have in mind for this workshop is about the different applications involving Gaussian processes and Gaussian fields. Let us give some example: periodicity detection by Fourier basis (using the self-reproducing Hilbert space) or the modelisation of the retina of the eye (with different parameters in function of the illness of the eye).

The second idea would be to enrich the model with latent variable. These are classical tools now in machine learning for regression and classification. Its variant, the Gaussian process dynamical model, has been used in computer vision for motion analysis and dynamical texture synthesis. Among these models, we find the stochastic differential equations (with or without latent variable). We have in mind the example of Kalman-Bucy filter which realizes gaussian filtering. This model is used in sciences of ocean and athmosphere, in research about petroleum sources...

Other subjects of interest for the workshop are Gaussian Processes state-space model, short and long memory processes, without any restriction.

In the continuity of the First workshop on gaussian processes at Saint-Étienne, the aim of this workshop is to gather different researchers from different communities working in the area of the Gaussian Processes, from the theoretical point of view to the applications.

More information on http://tugaut.perso.math.cnrs.fr/workshop02.html

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