* Goal: to assign data to discrete classes or categories. 

* Overview of unsupervised classification

* Overview of supervised classification

* Performance metrics: Completeness, Contamination, Precision, Recall 

* Unsupervised methods: clustering methods for unsupervised classification

* Supervised methods:

- K-Nearest Neighbours

- Support Vector Machines (SVM)

- Decision Trees

- Random forests

* Semi-supervised methods

Computational exercises in optimisation

* Goal: minimum/maximum search of cost function, likelihood, posterior, etc

* Approaches

- Brute force (curse of dimensionality)

- Gradient descent and its generalizations: Stochastic Gradient Descent (SGD) with mini-batches; Adding momentum (GDM); AdaGrad (Adaptive Gradient Algorithm); RMSprop; ADAM (Adaptive Gradient Algorithm)

- Markov Chain Monte-Carlo (MCMC, also gives confidence intervals)

- Integrated Nested Laplace Approximations (INLA, also gives confidence intervals)

Computational exercises in maximum likelihood and bayesian inference

* Statistical Inference: Frequentist and Bayesian views

* Bayes theorem revisited: Likelihood, prior, posterior, evidence

* Some properties: 

- inclusion of previous knowledge

- Updating the posterior with new knowledge

- Error propagation for free

* Maximum Likelihood Estimation (MLE)

- Detailed cases of Gaussian Homoscedastic and Heteroscedastic errors

* Bayesian addressing of Malmquist, Eddington and Lutz-Kelker biases