MA8701 Final oral exam

Final individual oral exam is on May 10, 15 and 22 in 822, sentralbygg 2. All students have signed up for the exam and have now a time slot.

The exam will last approximately 30 minutes. There is a chalk board in the room.

Choose one of five topics (to be given below), and prepare a short presentation (no slides) for the first part of the oral exam. Duration should be maximum 10 minutes (thus, you have to select carefully what to focus on), and you are allowed to use notes. You may write by hand.

Preparing a presentation is not compulsory, but if you have not prepared a presentation the same questions will be asked in the first part of the oral exam.

1) Missing data We have discussed different methods for handling missing data, and the most complex of these is multiple imputation. Main elements of the multiple imputation method is the imputation model, the analysis model and use of Rubins´ rules for pooling of results.

a) If the imputation model is based on chained equations, what are the choices we need to make to run the model?

b) Let us say I have made $m$ complete datasets in a), and then I perform logistic regression as my analysis model. What do I do with the $m$ sets of regression estimates I have gotten?

c) What are challenges when using multiple imputation as part of a larger data analysis set-up?

2) Lasso regression is the answer to an L1 penalty-problem, and the L1 penalty has been used for several models in this course.

a) Write down the model and additional assumptions for a linear regression model with L1 penalty.

b) Explain how model parameters are estimated, and give properties of the parameter estimator.

c) Comment on changes needed when moving from the linear lasso regression to logistic lasso regression model.

3). Prediction vs. inference In MA8701 one aim has been to move from a focus on prediction to statistical inference.

a) Choose one situation where we have done this, and elaborate.

b) What are challenges, and what is gained by using statistical inference? (Hints for some situations: inference for the lasso, selective inference. Other situations exist.)

4) Ensembles An ensemble can be constructed in different ways. Assume that our aim is regression (to minimize squared loss) and we use regression trees (with binary splits) as base learners.

a) What are the main differences between a random forest and a gradient boosting tree? b) Which statistical principles (that we have learned about in this course) are used when moving from the gradient boosting tree to the xgboost? Hint: many are related to xgboost hyperparameters.

5) The Shapley values are used in explainable AI.

a) What is the philosophy behind the Shapley value?

b) The Shapley regression is a global method (also referred to as the LMG-method). How does it relate to the Shapley value?

c) What are challenges if you want to use Shapley values for prediction explanation for a black box model?

The remainder of the exam is answering questions from the course reading list. No notes are allowed.