Statistics Seminar by Maria D. Ruiz-Medina, the University of Granada, Spain

Abstract

This talk presents a morphological and deep asymptotic analysis of random neural networks, under some invariance properties, when input data lie on a manifold. The double spectral domain is considered for di- mension reduction, as a suitable structural complexity summary tool. For inference, an empirical Bayesian functional regression approach is adopted to approximate the predictive probability distribution of the Exceedance Field associated with the NNGF under moving levels. The methodological approach presented is implemented from samples of temporal correlated spherical functional data affected by additive spatiotemporal spherical Gaussian noise. In particular, an infinite–dimensional version of Gaussian Process Regression is obtained, covering the cases of weak–and strong–dependent functional data. Results are illustrated via simulations and real–data applications, considering the family of spatiotemporal covariance functions in the Gneiting class. 

The contents of this talk correspond to recent contributions presented by Ruiz-Medina in Modern Trends in Probability Theory and Mathematical Statistics IV (in honor of Professor Mykola/Nikolai Leonenko), as well as new advances on infinite-dimensional Gaussian process regression derived in the paper by Ruiz-Medina, Madrid, Torres-Signes and Angulo (2026).

References

Ruiz-Medina, M.D. (2026). The role of the double spectral white noise analysis in STRF asymptotic theory. International Workshop Modern Trends in Probability Theory and Mathematical Statistics IV in honor of Professor Mykola/Nikolai Leonenko. https://probability.knu.ua/moderntrends4/

Ruiz-Medina, M.D., Madrid, A.E., Torres-Signes, A. and Angulo, J.M.(2026). Time-adaptive infinite-dimensional Gaussian process regression on manifolds. arXiv:2603.21144.