# Statistical learning. Estimation, selection and inference

lstat2450  2021-2022  Louvain-la-Neuve

Statistical learning. Estimation, selection and inference
5.00 credits
30.0 h + 7.5 h
Q1
Teacher(s)
Pircalabelu Eugen;
Language
English
Prerequisites
LSTAT2011 Éléments de mathématiques pour la statistique
LSTAT2013 - Concepts de base en statistique inférentielle
LSTAT2120 Linear models
LSTAT2020 Logiciels et programmation statistique de base
Main themes
The course focuses on high-dimensional settings and on techniques to that allow for parameter estimation, model selection and valid inferential procedures for high-dimensional models in statistics.
Learning outcomes
 At the end of this learning unit, the student is able to : 1 With regard to the AA reference framework of the Master's programme in Statistics, general orientation, this activity contributes to the development and acquisition of the following AAs, as a matter of priority : 1.4, 1.5, 2.4, 4.3, 6.1, 6.2
Content
The class is focused on the presentation of key concepts of statistical learning and high-dimensional models such as:
• Statistical learning
• Challenges concerning high-dimensional models and differences from low-dimensional models
• Classical variable selection techniques for linear regression models: R2, adj.R2, Cp
• Information criteria selection: KL divergence, AIC/TIC/BIC derivation
• Cross-validation based selection: Leave-one-out and K-fold
• Under- and overfitting or the bias-variance trade-off
• Ridge shrinkage: theoretical properties, bias/variance trade-off, GCV
• Lasso shrinkage: regularization paths, LARS, coordinate descent algorithm, prediction error bounds, degrees of freedom for lasso, support recovery, stability selection, knock-offs; inference by debiasing, post-selection inference, Bayesian inference
• Extensions of Lasso: elastic net, group lasso, adaptive lasso, fused lasso
• Other techniques: sparse graphical models, sparse PCA, sparse Disriminant Analysis
Teaching methods
The class consists of lectures (30h) and exercises sessions (7.5h).
The classes and the TP are intended to be face to face.
Teaching language: English.
Evaluation methods
The evaluation for this course consists of three parts:
• During the semester, the student must hand-in 2 compulsory assignments (short, 1 to 2 pages maximum per assignment), counting for 20% of the final grade. The homework is to be solved individually or in groups of 2. A grade will be awarded per group.
• A project (written in French / English in min 5 and max 9 pages in the template on Moodle, annexes not included) which will illustrate statistical learning methods in a concrete case (30% of the points). The project is evaluated on the basis of the written report. The project is to be solved individually or in groups of 2. A score will be awarded per group.
• An oral exam (~ 45 min.) at which the lecturer will assess the knowledge of the student with respect to the materials covered during the class (50% of the points). If necessary the lecturer will also ask questions about the results and the methodology used for the report and for the homework.
The exact evaluation methods could be adapted according to the constraints linked to the sanitary conditions in force at the time of the exam sessions.
Online resources
Moodle website of the class : LSTAT2450 - Statistical learning. Estimation, selection and inference.
https://moodleucl.uclouvain.be/course/view.php?id=14890
Bibliography
• Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of  Statistical Learning: Data Mining, Inference, and Prediction. Springer.
• James, G., Witten, D., Hastie, T., and Tibshirani, R. (2014). An Introduction to Statistical Learning: With Applications in R. Springer
• Hastie, T., Tibshirani, R. and Wainwright, M. J. (2015). Statistical Learning with Sparsity: The Lasso and Generalizations. Chapman and Hall/CRC.
• Wainwright, M. J. (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge University Press.
• Bühlmann, P., van de Geer, S. (2011). Statistics for High-Dimensional Data. Springer.
Teaching materials
• Transparents du cours disponible sur moodle.
Faculty or entity
LSBA

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Statistics: General

Certificat d'université : Statistique et sciences des données (15/30 crédits)

Master [120] in Data Science : Statistic