## 1. Measure theory and probability theory (1)

- Sets and sigma-algebras
- Measurability and integrals
- Lp spaces and convergence theorems
- Product spaces and independence

## 2. Optimization theory (2-3)

- Convexity
- Derivatives and critical points
- Iterative methods for optimization
- M-estimators and optimization of random functions

## 3. Density estimation (4)

- Maximum likelihood estimation
- Finite mixture models and the EM algorithm
- Kernel density estimators
- Goodness of fit tests and misspecification

## 4. Regression analysis (5-6)

- Proper conditioning
- Conditional density functions
- Least squares estimators
- Regularization and constrained regression
- Conditional density estimation
- Finite mixture of experts models

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