Title: The Iterative Proportional Scaling Algorithm
Prof. Tamás Rudas, Eötvös Loránd University, Hungary.
Summary: IPS is a very flexible algorithm used to solve many problems for categorical data, including small area estimation in official statistics, post-stratification in survey research, maximum likelihood estimation of log-linear models and feature selection in machine learning. After presenting the common core of these problems, the IPS will be discussed in an exponential family context. In that setting, the IPS is related to a mixed parameterization and may be seen as an algorithm to combine the canonical parameters of one distribution with the mean value parameters of another. It will be shown, that for categorical data, the canonical parameters are conditional odds ratios and the mean value parameters are marginal distributions. A general proof of convergence given by Csiszár based on Kullback-Leibler projections will be sketched. Finally, in addition to the original IPS usually attributed to Deming & Stephan, variants and generalizations proposed by Darroch & Ratcliff, Della Pietra et al. and by Klimova & Rudas will be presented.
Title: Functional data and nonparametric modelling: theoretical/methodological/practical aspects
Prof. Frédéric Ferraty, Toulouse Jean Jaures University, France.
Summary: High-tech advances (automated medical monitoring system, connected objects, remote sensing, etc) provide data containing some continuum. The continuum may concerns the time but not only. For instance, in Chemometrics, spectrometers produce data where the continuum feature comes from the wavelength dimension. Consequently, a statistical unit may be a curve, a surface or any more complex mathematical object presenting at least one continuum feature. Such data are called functional data, where the word "functional" is the natural mathematical concept for handling continuum. The challenge is simple: extracting relevant information from datasets containing collections of curves, or surfaces or any other complex objects, most of the time combined with standard multivariate variables. All methodologies dealing with such functional data are gathered under the terminology Functional Data Analysis (FDA). The success of this exciting modern area of Statistics is mainly due to its ability to solve important theoretical problems while proposing original and relevant answers to practical issues coming from topical fields of applications (environmetrics, remote sensing, 3D-4D medical imaging, neuroscience, quantitative genetics, particle physics, astronomy, econometrics, etc). In this tutorial we propose mainly to focus on situations when one observes a response (scalar or functional variable) and functional predictor(s). The natural statistical question is very simple: are we able to predict correctly the response from the functional predictor(s) when one has no idea on the relationship between the response and functional predictor(s)? A suitable answer to this important statistical issue is the "functional nonparametric regression". The word "nonparametric" stands for any model requiring very few assumptions with respect to the relationship between the response and the predictor(s); the word "functional" reminds that the model has to handle functional data. So, the aim of this tutorial is to give an extensive overview on this statistical topic. In addition of some theoretical and practical key developments, real datasets complete the presentation in order to illustrate our purpose (benchmark datasets, hyperspectral image, forensic entomology in the context of criminology, etc).