The talks will take place virtually on 17th November 2023.
Abstracts
Director, Chair of Computational Mathematics
PI-ERC Advanced Grant DyCon Project
In this lecture we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning, Universal Approximation and Normalizing flows.
We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control.
We present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies.
This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill.
The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics.
This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Domènec Ruiz-Balet (IC, London), Martin Hernandez (FAU) and Antonio Alvarez (UAM).
Licenciada en Matemáticas-Universidad Autónoma de Madrid).
MBA por la Escuela de Negocios de Madrid. Especialidad en Marketing.
CEO y Fundadora de Conento, empresa líder en España en consultoría Analítica de Marketing.
En la intersección de las matemáticas, el marketing y la inteligencia artificial, encontramos una revolución en la forma en que las empresas se conectan con sus clientes. Las matemáticas proporcionan la estructura y precisión, el marketing aporta la estrategia y la creatividad, y la IA ofrece la capacidad de procesar grandes cantidades de datos y aprender de ellos. Juntos, estos campos están redefiniendo el panorama del marketing moderno, permitiendo campañas más personalizadas, decisiones basadas en datos y una comprensión más profunda del comportamiento del consumidor. Macarena nos hablará de todo ello, con su visión de futuro y su vista más allá de 2030.
Professor of Statistics at the University of Franche-Comté
Member of the Probability and Statistics team at the Besançon Mathematics Laboratory
Head of the Master's degree in Statistical Modeling in Besançon (2018-)
In surveys, model-assisted estimators and calibration estimators, based on auxiliary information, are commonly used to obtain efficient estimators of population totals/means. Nowadays, it is no longer unusual to face high-dimensional auxiliary information. Incorporating too many auxiliary variables in model-assisted and calibration estimators may lead to a loss of efficiency. In this talk, I will discuss the asymptotic efficiency of model-assisted estimators based on high-dimensional auxiliary data and show that they may suffer from an additional variability in certain conditions. I will also present two techniques for improving the efficiency of model-assisted estimator in a high-dimensional framework: the first is based on dimension reduction through principal components and the second is based on ridge-type penalization. The methodology is illustrated using a real-data set on the electricity consumption of households and businesses in Ireland.
This conference is supported by the following institutions/societies/projects: