Departamento de Matemáticas UAM

Machine learning in Madrid    (zoom)

Lunes, 24 de enero de 2022, 12-13h

Enlace: https://us06web.zoom.us/j/83094800012?pwd=K1ZXbXNYcFpLcUIrd0NPWkVaVEpEQT09

Ponente:   Alberto Suárez  (UAM)

Título:  Classification of functional data

Abstract:  Most machine learning methods assume that the instances used for induction are characterized by a vector of attributes. However, in many areas of application, there are problems in which more complex structures, such as functions, are the natural description of the data. Examples of these types of problems are medical diagnostic from continuous monitoring of vital signs, prediction of extreme weather from spatio-temporal meteorological data, or quality control in industrial processes. A possible approach is to make a multivariate representation of these data (e.g., by PCA, truncated basis expansions, or the identification of points of impact) and then apply standard multivariate machine learning algorithms. In this talk, we will describe a number of methods for classification that take into account the functional nature of such data. Their design makes use of the tools of functional data analysis (FDA), the branch of statistics that deals with random functions. In many cases, the infinite-dimensional nature of the data limits the applicability of standard predictors, such as logistic regression or discriminant analysis. The reason is that these depend on quantities (e.g. the inverse of the covariance matrix) that are ill defined in the infinite-dimensional case. These singularities are in fact at the origin of novel phenomena, such as near-perfect classification, that appear when functional data are used for induction.