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Advanced statistical models

Presentation

Introduction to statistical learning and to model selection

-Forecasting quality of a statistical model, notion of risk,

optimal rules, risk estimation with penalisation or by simulation

-Model selection and variable selection in linear models : AIC, BIC criterion, Ridge and Lasso methods

-Projection and regularisation methods : Splines, wavelet bases and thresholding, Reproducing  Kernel Hilbert Spaces

-Support Vector Machine for classification

-Kernel estimators in density or regression

-Introduction to kriging for spatial statistics

- Curves classification

 

Organisation:

-Lectures : 20H

-Practical work of applications on real data sets with the software R or Python’s libraries( Scikit Learn) : 18H

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

 

-Fitting statistical models in regression or classification in high dimension with various approaches

-Estimation of the prediction error

-Optimal model selection for prediction

-Application of statistical learning methods on real data sets

 

 The student will be able to:

 

-Fit and select a statistical model in high dimension for prediction purposes

- Implement statistical learning methods in high dimension on real data sets with the software R or Python’s libraries.

Needed prerequisite


Probability and statistics
Point processes, martingales
Elements of statistical modelling.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...