  The goal of these lecture notes is to review the problem of free energy
minimization as a unified framework underlying the definition of maximum
entropy modelling, generalized Bayesian inference, learning with latent
variables, statistical learning analysis of generalization,and local
optimization. Free energy minimization is first introduced, here and
historically, as a thermodynamic principle. Then, it is described
mathematically in the context of Fenchel duality. Finally, the mentioned
applications to modelling, inference, learning, and optimization are covered
starting from basic principles.
