For any convex function φ and integrable random variable X, φ(E[X]) ≤ E[φ(X)]; equality iff X is almost surely constant on the interior where φ is strictly convex. Jensen 1906. Tools: entropy inequalities (KL ≥ 0), EM algorithm…
For any convex function φ and integrable random variable X, φ(E[X]) ≤ E[φ(X)]; equality iff X is almost surely constant on the interior where φ is strictly convex. Jensen 1906. Tools: entropy inequalities (KL ≥ 0), EM algorithm…