Statistical Modeling and Machine Learning
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
IN2332 is a semester module in English language at Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
|Total workload||Contact hours||Credits (ECTS)|
|240 h||120 h||8 CP|
Content, Learning Outcome and Preconditions
1. Concepts in machine learning: supervised vs. unsupervised learning, classification vs. regression, overfitting, curse of dimensionality
2. Probability theory, Bayes theorem, conditional independence, distributions (multinomial, Poisson, Gaussian, gamma, beta,...), central limit theorem, entropy, mutual information
3. Generative models for discrete data: likelihood, prior, posterior, Dirichlet-multinomial model, naive Bayes classifiers
4. Gaussian models: max likelihood estimation, linear discriminant analysis, linear Gaussian systems
5. Bayesian statistics: max posterior estimation, model selection, uninformative and robust priors, hierarchical and empirical Bayes, Bayesian decision theory
6. Frequentist statistics: Bootstrap, Statistical testing
7. Linear regression: Ordinary Least Square, Robust linear regression, Ridge Regression, Bayesian Linear Regression
8. Logistic regression and optimization: (Bayesian) logistic regression, optimization, L2-regularization, Laplace approximation, Bayesian information criterion
9. Generalized Linear Models: the exponential family, Probit regression
10. Expectation Maximization (EM) algorithm with applications
11. Latent linear models: Principle Component Anlaysis, Bayesian PCA
- 1. remember the concepts of supervised and unsupervised learning and to implement cross-validation procedures
- 2. remember the concepts of Bayesian probabilities, of conditional and unconditional dependences
- 3. derive mathematically the models and inference procedures of Bayesian linear regression, Generalized linear models, Bayesian Principal Component Analysis, and k-means.
- 4. identify use cases of the above mentioned models
- 5. apply the above mentioned models using the R programming language
- 6. assess the performance and significance of their results
- 7. develop simple novel Bayesian models and inference procedure thereof for situations for which the above mentioned models do not apply.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||4||Statistical Modeling and Machine Learning (IN2332)||Gagneur, J.||
Tue, 14:00–17:00, MI 03.13.010
|UE||4||Exercise Statistical Modeling and Machine Learning (IN2332)||Gagneur, J.||
Fri, 12:30–15:30, MI 01.09.034
Fri, 12:30–15:30, MI 02.13.010
Learning and Teaching Methods
Description of exams and course work
There is a possibility to take the exam in the following semester.