A Tutorial on Bregman Projection in Statistics (opens in new tab)

A single geometric operation -- projecting a reference onto a constrained family under a Bregman divergence -- underlies a striking range of statistical methods. This tutorial develops the operation first as pure convex geometry, with no statistics attached. A strictly convex generator $G$ and its conjugate $F$ furnish two coordinate systems, a projection theorem with existence and uniqueness, and a Pythagorean {theorem}; the Pythagorean theorem...