Schedule & Abstracts

Control and Machine Learning :  Enrique Zuazua

Enrique Zuazua

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).

Model-assisted and calibration estimation in a high-dimension setting for survey data: Camelia Goga

Camelia Goga

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.