15.12 I was Participant1: It was held via single zoom meeting. he told the first question and then wanted me to put the camera down so he could see me writing the answers to the prepared papers. During talking he also wanted to find out how well i understood the topics. He helped if necessary. Afterwards i needed to send the pdf with fotos of the written pages. Q1:easy starter.. linear Model , how to calc beta's? (hat matrix..) What problems can happen? (near-sigularities -> expoding betas) What to do? i.E Shrinkage: -> Explain Diff Ridge & Lasso (how do get the betas zero?) Q2: SVM: separable case: how to solve that problem? what side contraints need to take care of Q3: what is the kernel trick? (some talking about projections and its inner dot product. OLD QUESTIONS _______________________________________ 19.12.2019. 11:00 Participant 1: Trees: Regression trees, classification trees. General idea, criterion to minimized, for both cases. What measures of node impurity are available? How to avoid overfitting (pruning). SVM: criterion for linearly separable, non-linearly separable case. Kernel trick, kernel functions. GAM: for regression. How does the model look like, what functions mimimize criterion. Participant 2: Mulitple regression model: Ordinary LS solution, how to arrive at it, what to do in near singularity of X^T X, R Ridge Regression, Lasso Regression, how does that look like, what is is different to OLS Spline regression: Criterion to minimize (with penalization of curvature), what functions do minimize this (natural cubic splines) 11:30 Participant 3: Define PCR and weighted least squares. Compare these two methods Define SVM for the linearly seperable and for the inseperable case. 04.02.20 - 10:00 Participant 1: SVM: SVM linear seperable and non seperable. Explain the optimization formula and how you get there for both, L_p, L_d, with constraints. Splines & Smooting Splines: Explain splines in general, i.e. knots, knot selection and df. Explain smoothing splines, optimization formula and general idea Participant 2: Logistic Regression: Explain logistic regression with focus on the two group case. Explain regression trees with focus on the splitting criteria. Participant 3: Explain Lasso and Ridge regression. Formulas, Lambda parameter, why does Lasso set coeficients exactly to 0, show it visually. The formula for beta^hat_ridge. LDA,QDA,GDA: What is the idea of LDA. What is the Bayesian Theorem what are its assumptions and formula (the phi formula). Formula for LDA and GDA. What are the components of LDA and how do you estimate them. Why can u estimate them? Random Forests: explain the Random Forest algorithm, bagging, selection of features, T_b, pi_bj, theta_bj 27.2.20 Participant 1: Smoothing Splines: What are splines, what is the criterion to optimize and the solution (formulas). How to determine Lambda/degrees of freedom. What does degrees of freedom mean in this context, why do we care about it? SVM: Write down the optimization criteria with side constraints, how we get the solution (Lagrange primal, dual function) and KKT conditions for the linearly separable and inseparable case. Why do we need the KKT conditions? What is the Kernel trick? <- For this question I started with basis expansions, and that we put the basis functions in a vector h(x) = (h_1(x), ..., h_M(x)) and define our hyperplane with that. Then I explained that h(x) is only involved in the inner product in the solution and that we don't need to define the basis functions if we have a Kernel function that returns a real value. That seemed to be what Prof. Filzmoser wanted to hear. Participant 2: Regression trees: Splitting criteria (formula), how to grow the tree and how long? Quality measure and cost complexity criterion (formula) PCR: Model, how to get principal components (formulas), solution for the estimated coefficients beta_hat (formula). Why do we need PCR, in what use cases might this be helpful (singularity of X^TX)?