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14th Seminar of the “D2 Seminar Series” – Florence Center for Data Science

March 25, 2022 @ 14:30 - 16:00

The Florence Center for Data Science is happy to present the 13th Seminar of the “D2 Seminar Series” launched by the FDS. The Seminar will be held online Friday 25th of March 2021, from 2.30-4 pm.

Brunero Liseo from the Department of Methods and Models for Economics, Territory, and Finance of the Sapienza University will present a seminar on “ABCC: Approximate Bayesian Conditional Copulae (with Clara Grazian and Luciana Dalla Valle)” and Ernesto De Vito from the Department of Mathematics of the University of Genova will present a seminar on “Understanding Neural Networks with Reproducing Kernel Banach Spaces“.

Register in advance for this webinar:
https://us02web.zoom.us/webinar/register/WN_KFoLkeSfT3-kzWLK2mwHPA

After registering, you will receive a confirmation email containing information about joining the webinar.

Speaker: Brunero Liseo – Department of Methods and Models for Economics, Territory, and Finance of the Sapienza University
Title: ABCC: Approximate Bayesian Conditional Copulae (with Clara Grazian and Luciana Dalla Valle)
Abstract: Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar’s theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the product of the marginal distributions and a copula function that captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however, extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the copula function, especially when one does not have enough information to select the copula model. Recent advances in computational methodologies and algorithms have allowed inference in the presence of complicated likelihood functions, especially in the Bayesian approach, whose methods, despite being computationally intensive, allow us to better evaluate the uncertainty of the estimates. In this work, we present several Bayesian methods to approximate the posterior distribution of functionals of the dependence, using nonparametric models which avoid the selection of the copula function. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.
 
Speaker: Ernesto De Vito – Department of Mathematics of the University of Genova
Title: Understanding Neural Networks with Reproducing Kernel Banach Spaces
Abstract: Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. The talk is devoted to showing how the theory of reproducing kernel Banach spaces can be used to characterize the function spaces corresponding to neural networks. In particular, I will show a representer theorem for a class of reproducing kernel Banach spaces, which includes one hidden layer neural network of possibly infinite width. Furthermore, I will prove that, for a suitable class of ReLU activation functions, the norm in the corresponding reproducing kernel Banach space can be characterized in terms of the inverse Radon transform of a bounded real measure. The talk is based on on joint work with F. Bartolucci, L. Rosasco and S. Vigogna.

Details

Date:
March 25, 2022
Time:
14:30 - 16:00
Event Category:

Organizer

Florence Center For Data Science
View Organizer Website

Venue

Online