Post-selection Inference: Lasso & Group Lasso
| Název práce v češtině: | Povýběrová Inference: Lasso & Skupinové Lasso |
|---|---|
| Název v anglickém jazyce: | Post-selection Inference: Lasso & Group Lasso |
| Klíčová slova: | Povýběrová inference, Lasso, Skupinové Lasso, L1 regularizace, Lasso signifikance; |
| Klíčová slova anglicky: | Post-selection inference, Lasso, Group Lasso, L1 regularization, Lasso significance; |
| Akademický rok vypsání: | 2015/2016 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra pravděpodobnosti a matematické statistiky (32-KPMS) |
| Vedoucí / školitel: | doc. RNDr. Matúš Maciak, Ph.D. |
| Řešitel: | Mgr. Vojtěch Bouř - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 14.11.2015 |
| Datum zadání: | 14.11.2015 |
| Datum potvrzení stud. oddělením: | 01.03.2016 |
| Datum a čas obhajoby: | 14.06.2017 00:00 |
| Datum odevzdání elektronické podoby: | 11.05.2017 |
| Datum odevzdání tištěné podoby: | 12.05.2017 |
| Datum proběhlé obhajoby: | 14.06.2017 |
| Oponenti: | doc. Mgr. Michal Kulich, Ph.D. |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| [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. |