Tutorial: Variational Inference, (Not So) Approximate Bayesian Techniques, and Applications (Part 1 of 2)

Part I Approximate Bayesian Techniques Variational Bayes Variational Free Energy Variational Bayes (VB) Mean field and EM algorithms Expectation Propagation Factor Graph models Bethe Free Energy Belief Propagation Expectation Propagation Convergent Alternating Constrained Minimization ADMM Algorithm unfolding Relation to Deep NNs LMMSE case: multistage Wiener Filter Compressed Sensing LASSO, OMP etc. Sparse Bayesian Learning (SBL) Part II Generalized Linear models xAMP (AMP, GAMP, VAMP, GUAMP,…) convergent GAMP Large System Analysis (iid, Haar) Bayes optimality Stein’s Unbiased Risk Estimation SBL example: EM, VB, SURE Part III Bilinear models Cell-Free Massive MIMO setting MAP and MMSE estimates CRB variations EP variations: Factor Level, Variable Level Part IV Adaptive Kalman filtering Dynamic SBL setting Bayesian CRB EM, VB,…., applied to Kalman filtering