TILM3622 Advanced Regression Analysis and Statistical Learning (6 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Grading scale:
0-5
Description
This course contains various extensions of linear and generalized linear models and their connections to statistical learning. These are, among others, parametric nonlinear and nonparametric regression functions and the methods connected to model selection and robust estimation. In statistical learning (cf. machine learning), we emphasize a stronger emphasis on statistics and statistical properties of the methods, with a special attention paid on the predictive performances of the methods. The objective of this course is generally to give starting points for more advanced statistical analyses with statistical learning methods such as various machine learning and neural networks algorithms.
The methods of this course are common and suitable for the analysis of a wide range of applications. In the term paper, it is possible to specialize according to one's own interest (e.g., minor or major studies) on the analysis of datasets in a specific application field.
Learning outcomes
After the course, the student masters various extensions of linear and generalized linear models. These are, among others, the following methods and methodological contexts:
- How to construct predictions (forecasts), select loss function and predictive model
- Cross-validation and the idea of bootstrap
- Classification-based models and methods: Logistic regression and linear discriminant analysis
- Shrinkage and penalization-based methods, such as ridge and lasso regression models
- Nonparametric regression functions and nonlinear regression models
Additional information
For statistics and mathematics major students, this course is also part of the Bachelor's level optional module "Biometrian sovellusalueiden opintokokonaisuus tilastotieteilijöille ja matemaatikoille" (Applications of Biometrics for Statisticians and Mathematicians") and "Rahoituksen opintokokonaisuus tilastotieteilijöille ja matemaatikoille" (Finance Study Module for Statisticians and Mathematicians").
The course is also in the UTUGS programme as a special course. In this case, it is recommended to first take the course TILM3627 Statistical learning: Boot camp (1 ECTS, also in the UTUGS programme).
Description of prerequisites
Students are expected to have the basic knowledge of linear regression analysis (including the basics of statistical inference), or introductory econometrics in economics and finance, and the prerequisites for those courses.
Statistics minor students can also benefit from completing the course TILM3627 Statistical learning: Boot camp (1 ECTS) before this course.