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Optimization using Graphical Models

Prof. Giulio Colavolpe - 2 CFU

Semester: second

Topic 1: Basics on convex optimization (Locatelli) Definitions of convex functions and sets. Brief sketches about complexity and algorithms. Constraint qualifications. Optimality conditions (KKT). Lagrangian duality.

Topic 2: Bayesian inference and graphical models (Colavolpe) Bayesian Networks and Markov Random Fields: Inference in general Graphs. Variational Inference techniques in Machine Learning and Artificial Intelligence: Belief Propagation (BP) and Loopy Belief Propagation Factor graphs and sum product algorithm: general framework and applications to communications.

Topic 3: Variational Inference and the Free Energies methods of Physics (Vannucci) Approximate Inference and factorized distributions. Variational mixtures of Gaussians. Exponential Family distributions. Variational message passing. Expectation Propagation and its implementation om graphs. Energy functions and their minimization schemes. Variational average energy and variational entropy; Gibbs and Helmholtz free energies. Stationary conditions for the Bethe free energy and its connections with Loopy belief Propagation. The Mean Field approximation.

Topic 4: Graphical models for optimization - Trajectory planning and power control (Consolini) Speed and trajectory planning problems, dynamic programming. Power control in radio systems. Reduction of previous problems to a standard form and definition of the associated graph. Graph-based solution algorithms.

Pubblicato Martedì, 20 Aprile, 2021 - 09:42 | ultima modifica Martedì, 20 Aprile, 2021 - 09:43