In this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection.
In-class exercisesA few times during the course, there will be in-class exercise sessions instead of a normal lecture. During those sessions, we will work with jupyter notebooks and R. These are provided in this Github repository.
If you are a PhD student who needs ETH credit points, the submission of the solutions is mandatory. If this applies to you, please email your solutions to Loris Michel or place them in the corresponding tray in HG J 68. Students who need ECTS credit points have to take the exam.
|Series 1||Solutions 1||TBA|
- Script by Jonas Peters and Nicolai Meinshausen.
- Peters, Janzing and Schölkopf (2017). Elements of Causal Inference. MIT Press.
- Freedman, Pisani and Purves (2007). Statistics. Fourth edition. Chapters 1-2.
- Maathuis, Drton, Lauritzen and Wainwright (2019). Handbook of Graphical Models. CRC Press.
- Shalizi. Advanced Data Analysis from an Elementary Point of View. Chapters 20-25.
- Højsgaard, Edwards and Lauritzen (2012). Graphical Models with R.
- Pearl (2009). Causal inference in statistics: An overview.
- Spirtes, Glymour and Scheines (2000). Causation, Prediction and Search. MIT Press.
- Pearl (2009). Causality: Models, Reasoning and Inference. Wiley.
- Pearl, Glymour and Jewell (2016). Causal Inference in Statistics: A Primer. Wiley.
- Koller and Friedman (2009). Probabilistic Graphical Models. MIT Press.