| additional remarks |
0. Univariate and simple multivariate calculus and summary of linear algebra with intuitive explanations
1. Concepts in machine learning: supervised vs. unsupervised learning, classification vs. regression, overfitting, curse of dimensionality
2. Probability theory, Bayes theorem, conditional independence, distributions (multinomial, Poisson, Gaussian, gamma, beta,...), central limit theorem, entropy, mutual information
3. Generative models for discrete data: likelihood, prior, posterior, Dirichlet-multinomial model, naive Bayes classifiers
4. Gaussian models: max likelihood estimation, linear discriminant analysis, linear Gaussian systems
5. Bayesian statistics: max posterior estimation, model selection, uninformative and robust priors, hierarchical and empirical Bayes, Bayesian decision theory
6. Frequentist statistics: Bootstrap, Statistical testing
7. Linear regression: Ordinary Least Square, Robust linear regression, Ridge Regression, Bayesian Linear Regression
8. Logistic regression and optimization: (Bayesian) logistic regression, optimization, L2-regularization, Laplace approximation, Bayesian information criterion
9. Generalized Linear Models: the exponential family, Probit regression
10. Expectation Maximization (EM) algorithm with applications
11. Latent linear models: Principle Component Anlaysis, Bayesian PCA |