Approximate Majorization

Understand

Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target.

• Here we introduce a notion of approximate majorization.
• For any distribution, and given a distance $\delta$, we find the approximate distributions which majorize (are majorized by) all other distributions within the distance $\delta$.
• We call these the steepest and flattest approximation.