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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