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18 months ago

Dustin
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In order to define the Tsallis-Shannon entropy which they will use as a regularizer the authors define what they call the Tsallis-perspective (H) of a convex function h. The issue is that H is not always convex. However, given a certain condition on h given in Lemma 1 in section 3.1 we get a lower bound on the hessian of H which implies that H is convex.

What is a geometric interpretation of the inequality in Lemma 1?

Alternatively is there a natural calculation in which the left hand side of the inequality shows up?

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