Bayesian cognition - WPMCCOB0

Goal(s)

Both living organisms and robotic systems must face the same central difficulty: How to survive while being ignorant? How can they use an incomplete and uncertain model of their environment to perceive, infer, decide, learn and act efficiently?

Indeed, any model of a real phenomenon is incomplete: there are always some hidden variables, not taken into account in the model, that nevertheless influence the phenomenon. The effect of these hidden variables is that the model and the phenomenon never behave exactly alike. Uncertainty is the direct and unavoidable consequence of incompleteness. A model may not foresee exactly the future observations of a phenomenon as these observations are biased by the hidden variables. It may neither predict exactly the consequences of its decisions.

Probability theory, considered as an alternative to logic to model rational reasoning, is the perfect mathematical framework to face this difficult challenge. Learning is used in a first step to transform incompleteness into uncertainty, inference is then used to reason and take decisions based on the probability distributions constructed by learning. This so-called subjectivist approach to probability allows uncertain reasoning as complex and formal as the ones made using logic with exact knowledge.

The main objective is to provide and introduction to this approach, from theoretical foundations to practical algorithms, and from central nervous system models to industrial applications.

Content(s)

Content summary:

• Theoretical foundation and justifications: how are probabilities an alternative to logic as a model of rational reasoning?
• Formalism and models: how to build a Bayesian model?
• Algorithms and inference: how are performed inference and learning? (Here, the description stays at a general audience level: we do not delve into the detail of Baum-Welch learning, MCMC or variational methods, for instance, contrary to what would be done in an algorithmic class).
• Detailed examples of Bayesian models used in life sciences, robotics, and industrial applications.
• Application of the Bayesian formalism for model comparison and selection.

No particular prerequisite, except for a general formation in mathematics and computer science. A M1 class in Bayesian methods exists in Grenoble: it is a plus, but far from necessary. Class is given in French, slides are in French or English, accompanying material in English. During lectures, questions can be asked and answered in English.