# Bayesian Reasoning with Graphical Models

This course motivates and introduces graphical models (with special attention to Bayesian networks) as well consolidated and popular tools with the ability to represent knowledge under uncertainty and reason with it, one of the main challenges in building intelligent systems in Artificial Intelligence. Uncertainty is modelled with probability theory and reasoning is based on Bayes’ rule. Bayesian networks represent factorizations of joint probability distributions. Nodes represent the variables of the domain and links represent the properties of conditional dependences and independences among the variables. The course will provide an in-depth exposition of theoretical and practical underpinnings. The course starts explaining the meaning of these networks to model both causal and non-causal knowledge under uncertainty, and both from a structural viewpoint (qualitative) and from a parametric viewpoint (quantitative). The following step is to query the network about different issues of interest, i.e. to make inferences from evidence that is being gathered. For example, we can ask for the diagnosis of a disease or for the most probable explanation of the observed evidence. The inference algorithms can obtain an exact or an approximate answer, the latter being computed via e.g. Monte Carlo simulation. The network is built with the aid of a domain expert, but it can also be induced from a database. This calls modern learning algorithms including parameter learning and structure learning techniques. Finally, additional topics include a number of successful real-world applications in different areas.

Pedro Larrañaga |

Activities |
Hours |

Theoretic class attendance |
2 per week |

Practical class attendance |
1 per week |

Preparing the practical classes |
1 per week |

Study |
30 hours |

Develop the projects |
15 hours |

Oral presentations |
12 hours |

Following the on-line classes |
3 hours |

**PRERREQUISITES **

Familiarity with basic concepts of probability theory (including Bayes’ rule, multinomial and normal distributions).

**DESCRIPTION**

This course motivates and introduces graphical models (with special attention to Bayesian networks) as well consolidated and popular tools with the ability to represent knowledge under uncertainty and reason with it, one of the main challenges in building intelligent systems in Artificial Intelligence. Uncertainty is modelled with probability theory and reasoning is based on Bayes’ rule. Bayesian networks represent factorizations of joint probability distributions. Nodes represent the variables of the domain and links represent the properties of conditional dependences and independences among the variables. The course will provide an in-depth exposition of theoretical and practical underpinnings.

The course starts explaining the meaning of these networks to model both causal and non-causal knowledge under uncertainty, and both from a structural viewpoint (qualitative) and from a parametric viewpoint (quantitative). The following step is to query the network about different issues of interest, i.e. to make inferences from evidence that is being gathered. For example, we can ask for the diagnosis of a disease or for the most probable explanation of the observed evidence. The inference algorithms can obtain an exact or an approximate answer, the latter being computed via e.g. Monte Carlo simulation. The network is built with the aid of a domain expert, but it can also be induced from a database. This calls modern learning algorithms including parameter learning and structure learning techniques. Finally, additional topics include a number of successful real-world applications in different areas.

**OBJETIVES**

- To understand the meaning and chances of probabilistic graphical models as a leading technology for reasoning with knowledge under uncertainty.
- To provide skills in different kinds of reasoning with these models: deductive, diagnostic, intercausal, or any combination of them.
- To construct a Bayesian network both with the aid of an expert or learning it from a data set.
- To address tasks as decision making, classification and data mining.
- To know existent salient applications and discover/suggest new ones.
- To use standard software (academic and commercial).

**MATERIAL**

Lectures, exercises, exams and projects proposal.

**EVALUATION ACTIVITIES AND EXERCISES**

Homeworks, project (40%), oral student presentation (30%), quiz with background material (30%). Participation in class and attendance will be valued.

Course Contents