Řídké regresní modely
| Thesis title in Czech: | Řídké regresní modely |
|---|---|
| Thesis title in English: | Sparse regression model |
| Key words: | regresný model|regularizace|odhadování s penalizaci|řídke odhady |
| English key words: | regression model|regularization|penalized estimation|sparse estimates |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Matúš Maciak, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 26.10.2022 |
| Date of assignment: | 26.10.2022 |
| Confirmed by Study dept. on: | 23.01.2023 |
| Date and time of defence: | 10.06.2024 08:30 |
| Date of electronic submission: | 02.05.2024 |
| Date of submission of printed version: | 02.05.2024 |
| Date of proceeded defence: | 10.06.2024 |
| Opponents: | prof. RNDr. Ivan Mizera, CSc. |
| Guidelines |
| Cieľom práce je popísať niektoré jednoduché regresné modely postavené a odhadované na princípe riedkých parametrov (resp. odhadov)
a regularizovanej minimalizácie vhodnej objektivnej funkcie (t.j., odhadovanie s penalizačným členom). Autor/autorka sa oboznámi so základnou problematikou, teoretickými vlastnosťami aj praktickou implementáciou niektorých základných postupov. |
| References |
| [1] Fan, J., Lv, J. and Qi, L. (2011). "Sparse high-dimensional models in economics". Annual Review of Economics 3:291–317.
[2] Harchaoui, Z. and Lévy-Leduc, C. (2010). "Multiple Change-Point Estimation With a Total Variation Penalty". Journal of the American Statistical Association, 105(492):1480-1493. [2] Krämer, N., Schäfer, J., and Boulesteix, A.L. (2009). "Regularized estimation of large-scale gene association networks using graphical Gaussian models". BMC Bioinformatics , 10(2009): 1--24. [3] Tibshirani, R. (1996). "Regression Shrinkage and Selection Via the Lasso". Journal of the Royal Statistical Society: Series B (Methodological), 58:267--288. |
| Preliminary scope of work in English |
| The author of the thesis will discuss some basic regression models based on sparse parameter estimates and regularized estimation (minimization with a penalty term).
Some basic statistical properties of the sparse estimates will be discussed and derived. Empirical comparisons will be provided as well. |