[Probabilidad-Estadistica-Seminario] Seminario de Probabilidad y Estadística - Jean-Marc Azaïs (Université de Toulouse)

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Seminario de Probabilidad y Estadística
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Título: "The second maximum  of a gaussian random field and statistical application to sparse models."

Expositor: Jean-Marc Azaïs (Université de Toulouse)

Resumen:
 
Arising from continuous sparse kernel regression, we introduce the concept of
the so-called second maximum of a Gaussian random field. This second maximum
proves to be a valuable means for characterizing the distribution of the
maximum. In this paper, we use an ad-hoc Kac Rice formula to derive the explicit
form of the distribution of the maximum of a Gaussian random field, conditional
to the second maximum and the so-called random part of the Riemannian Hessian.
This method leads to an exact testing procedure based on the evaluation of
spacing between these maxima, referred to as the spacing test.    In addition,
if the variance-covariance function of the Gaussian random field is known up to
some scaling factor, we derive an exact studentized version of our testing
procedure called $t$-spacing test. We illustrate that the ($t$-)spacing tests
can be used to detect sparse alternatives in Gaussian symmetric tensor,
continuous sparse deconvolution, and two-layers neural networks with smooth
rectifier.
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Viernes 1/12 a las 10:30, Facultad de Ingeniería, salón 705 (salón marrón).

Contacto: Alejandro Cholaquidis - acholaquidis en hotmail.com
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https://salavirtual-
udelar.zoom.us/j/88544669179?pwd=UlBHdWRWdEZVMGw0akpPeEd0VWJzZz09

Página del  seminario : https://pye.cmat.edu.uy/ seminario

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Canal de youtube: https://www.youtube.com/channel/UCOPZEOrLSAYPz2qCAL-KqMg/about
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