Least Absolute Shrinkage and Selection Operator Method
| Thesis title in Czech: | Regresní metoda lasso |
|---|---|
| Thesis title in English: | Least Absolute Shrinkage and Selection Operator Method |
| Academic year of topic announcement: | 2016/2017 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Institute of Economic Studies (23-IES) |
| Supervisor: | RNDr. Michal Červinka, Ph.D. |
| Author: | hidden - assigned by the advisor |
| Date of registration: | 09.11.2016 |
| Date of assignment: | 09.11.2016 |
| Date and time of defence: | 14.06.2017 09:00 |
| Venue of defence: | Opletalova - Opletalova 26, O105, Opletalova - místn. č. 105 |
| Date of electronic submission: | 17.05.2017 |
| Date of proceeded defence: | 14.06.2017 |
| Opponents: | PhDr. Marek Rusnák, Ph.D. |
| URKUND check: | |
| Guidelines |
| The lasso (Least Absolute Shrinkage and Selection Operator) [1] is a method used to estimate important variables in models which work with high dimensional data. The lasso is a penalized regression technique which uses l1-norm (absolute value) penalization and it is based on minimization of the least-squares objective function which includes l1-penalty term. This technique performs both regularization and variable selection. We introduce related penalization techniques, namely, the so-called best subset selection method, ridge regression method and elastic net method.
The main goal of this bachelor thesis is to illuminate application of the lasso method when analyzing real economic data. We will employ the R software for numerical experiments. We shall compare the lasso estimator with several other types of estimators based on minimization of mean squared error. |
| References |
| [1] Tibshirani, R. Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society. Vol.58, No.1, 267-288, 1996.
[2] Jacob, L., Obozinski, G., and Vert, J.P. Group lasso with overlap and graph lasso. Proceeding ICML ’09 Proceedings of the 26th Annual International Conference on Machine Learning, 2009. [3] Buehlmann, P., Geer, S. Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Berlin Heidelberg, 2011. [4] Hastie, T., Tibshirani, R., Wainwright, M. Statistical Learning with Sparsity: The Lasso and Generalizations. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, 2015. [5] Belloni, A., Chernoyhukov, V., Hansen, Ch. High-Dimensional Methods and Inference on Structural and Treatment Effects. Journal of Economic perspectives, vol.28, no.2, 2014. [6] Zou, H. The Adaptive Lasso and Its Oracle Properties. Journal of the American Statistical Association, Volume 101, Issue 476, 2006. |
| Preliminary scope of work |
| Outline:
1. Introduction 2. Lasso regression method 3. Modifications of lasso and theoretical comparison 4. Data analysis and numerical comparison 5. Conclusion |
| Preliminary scope of work in English |
| Outline:
1. Introduction 2. Lasso regression method 3. Modifications of lasso and theoretical comparison 4. Data analysis and numerical comparison 5. Conclusion |