Model-based machine learning

• Explain central concepts in model-based machine learning, including probabilistic graphical models (PGMs), Bayesian inference and belief propagation
• Examine use cases for different PGMs and distinguish their underlying assumptions
• Implement PGMs in a probabilistic programming language (e.g. Pyro or Stan)
• Recognise practical data modelling aspects, like overfitting, system (e.g. spatial-temporal) dynamics, conditional independence, imputation, conjugate prior
• Evaluate quality of different models for given a problem and dataset
• Relate existing problems and data with modelling approaches to tackle them
• Formulate new models given a problem and data
• Develop and present a project based on a PGM
• Present, and be able to argue for, a project based on a PGM

This course will have lectures with slides and with laboratory work using interactive tools (Jupyter notebooks in Python using a probabilistic programming language like Pyro or STAN). Students will always work manually each module, during and after the theoretical class, to assimilate new concepts. It is designed to be incremental, and strongly supported with practice.

Modules: 
– Review of basics – random variable, probability distributions, Bayes Theorem 
– Probabilistic Graphical Models foundations – Bayesian networks, factorization,
D-separation, conditional independence
– Probabilistic Graphical Models – Generative models, Representing your own problem 
– Different models – Regression, Classification, Hierarchical Models, Temporal models, Generative models, Gaussian Processes
– Inference – Exact Inference
– Inference – Markov Chain Monte Carlo 
– Inference – Variational Inference
– Advanced topics

02806/02450/02807/42184/02402/02403, Fundamental statistics and probability (e.g. 42585 Business Analytics); knowledge of computer programming (e.g. Python, R, Matlab, Julia, C++, Java).

Lectures and practical laboratories with iPython notebook