Variational principle for probabilistic learning Yet another justification More simplification of updates for mean-field family Examples Dirichlet Process Mixture On minimization of divergence measures Energy minimization justifications Variational learning with exponential family Mean parametrization and marginal polytopes Convex dualities The log-partition function and conjugate duality Belie...

An entropic version of Liouville’s Theorem is defined in terms the conjugate variables (“hyperbolic position” and “entropic momentum”) an Hamiltonian. It used to derive Holographic Principle as applied holomorphic structures that represent maximum entropy configurations. The Bekenstein-Hawking expression for black hole a consequence. Based on commutator derived from same variables, Uncertainty ...