• Quem: Philippe Mahey

• Onde: Praia de Botafogo, 190 - sala 317

• Quando: 21 de Março de 2019 às 16h

We present an introduction to optimization techniques for computational statistics, data analysis and machine learning in the context of the celebrated ‘Big Data’ environment. After briefly recalling some of the main challenges of modern Data Analysis, we focus on the necessity to prepare and clean the huge amount of data collected before processing it, which is exactly where specially tailored optimization algorithms may be useful. The basic data analysis task is thus to identify a mapping between the data elements and a small set of outputs (clusters, labels,...), the latter being used for further analysis of the data set or for predicting the influence of future data elements. The huge dimension of the original data set is coupled with additional difficulties like noisy perturbations, over-fitting, missing data or labels, and online learning [1]. Most optimization models are extensions of least-square fitting with additional regularization terms, a common example being

                                                                              

where the l1 norm will induce sparsity and the l2 norm will reduce the sensitivity to noise [2]. We survey some elementary optimization algorithms from accelerated gradient method 'a la Nesterov' to coordinate-descent algorithms and Augmented Lagrangians. In the last section, we focus on monotone operator splitting techniques which have become very popular in the last decade for that purpose [3].From the classical ADMM (Alternate Direction Method of Multipliers) introduced in the 70's for decomposing nonlinear variational inequalities to recent Proximal Decomposition and blockiterative fixed-point methods, we show the main features and performance limits of these new trends for data analysis and machine learning.

References: [1] P. Buhlmann, S. Van De Geer, Statistics for High-Dimensional Data : Methods, Theory and Applications, Springer V, 2011. [2] R. Tibshirani, Regression shrinkage and selection via the LASSO, J. Royal Stat. Soc. B 58, pp. 267288, 1996. [3] A. Lenoir and P. Mahey, A survey on monotone operator splitting and decomposition of convex programs, RAIRO Operations Research 51, 2017

*Texto informado pelo autor. 

 

OBSERVAÇÃO PARA VISITANTES: 

A presença é gratuita e não exige confirmação. A FGV não permite a entrada de pessoas vestindo bermuda e/ou chinelos.