Post-selection Inference: Lasso & Group Lasso
| Thesis title in Czech: | Povýběrová Inference: Lasso & Skupinové Lasso |
|---|---|
| Thesis title in English: | Post-selection Inference: Lasso & Group Lasso |
| Key words: | Povýběrová inference, Lasso, Skupinové Lasso, L1 regularizace, Lasso signifikance; |
| English key words: | Post-selection inference, Lasso, Group Lasso, L1 regularization, Lasso significance; |
| Academic year of topic announcement: | 2015/2016 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Matúš Maciak, Ph.D. |
| Author: | Mgr. Vojtěch Bouř - assigned and confirmed by the Study Dept. |
| Date of registration: | 14.11.2015 |
| Date of assignment: | 14.11.2015 |
| Confirmed by Study dept. on: | 01.03.2016 |
| Date and time of defence: | 14.06.2017 00:00 |
| Date of electronic submission: | 11.05.2017 |
| Date of submission of printed version: | 12.05.2017 |
| Date of proceeded defence: | 14.06.2017 |
| Opponents: | doc. Mgr. Michal Kulich, Ph.D. |
| Guidelines |
| Variable selection and estimation via various LASSO approaches becomes very popular in recent statistical modelling especially if the number of available variables and thus the number of parameters to estimate is large. On the other hand, statistical properties for such estimates are still not well established. For example, two years ago it was not even clear what should be the appropriate degrees of freedom for such models.
The idea of this theses is to summarize recent developments in the post-selection inference in two most popular LASSO methods: classical LASSO selection and group LASSO selection. Different testing procedures were recently proposed but the finite sample properties are still to be investigated yet. The performance of the available methods can be tested using some real data example or some simulations instead. |
| References |
| [1] Lockhart, R., Taylor, J., Tibshirani, R.J., and Tibshirani, R. (2014). A Significance Test for the Lasso. Annals of Statistics, Vol. 42, No. 2, 413-468.
[2] Lee, J.D., Sun, D.L., Sun, Y., and Taylor J.E. (2013). Exact post-selection inference, with application to the lasso. arXiv:1311.6238 [math.ST]. [3] Tibshirani, R.J. and Taylor, J. (2012). Degrees of Freedom for LASSO Problems. The Annals of Statistics, Vol.40, No.2, 1198-1232. [4] Zhao, P. and Yu, B. (2006). On Model Selection Consistency of LASSO. Journal of Machine Learning Research, No.7, 2541-2563. |