This repo contains the R codes and the report of the research internship I did for a period of 4 months for the validation of my Master 1 in Statistics and Data Sciences (SSD). This internship was supervised:
- Sana Louhichi : University Professor at Grenoble Alpes University and Researcher at the Jean Kuntzmann Laboratory (CNRS)
- Didier A. Girard : Senior Researcher at Laboratory Jean Kuntzmann (CNRS)
- Karim Benhenni : Associate Professor at Grenoble Alpes University and Researcher at the Jean Kuntzmann Laboratory (CNRS) The theme of this internship is :
Model selection or validation in statistical learning is usually based on the ability to modeling for reasons of data interpretation or model prediction accuracy in competition. With regard to prediction, it is important to make an error estimate for future data. For penalized regressions such as LASSO, Ridge and Elastic-net, the estimation of this error often involves the observation of its curve as a function of the smoothing parameter or penalty generally noted. The method of cross-validation (which consists in dividing the training sample into several parts called folds) is a technique simple and intuitive to estimate the prediction error for new data. In large dimension i.e. in the case where the number of explanatory variables (p) is of the same order or more observations (n), this technique suffers from an enormous bias when the number of observations is greater of folds is small. Thus motivated by the lowest bias of the most extreme form of validation the Leave-One-Out (LO), the article "A scalable estimate of the extra-sample prediction error via approximate leave-one-out" [RM18] offers the Approximate Leave-One-Out (ALO) for a wide range of class of regularised estimators. This approximation considerably reduces time, resources and costs. calculation and with some assumptions about the data, the results obtained converge with those of the LO with a high probability when n, p become large. In this report we discuss the results obtained in [RM18] and we redo a large part of their simulations, and then we will make illustrations not included in [RM18] using the simulated data and we will end up with an perspective on future work.
Our work and codes are based on :
[RM18] Kamiar Rahnama Rad and Arian Maleki. A scalable estimate of the extra-sample prediction error via approximate leave-one-out. arXiv : Methodology, 2018.