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google / bi-tempered-loss

Robust Bi-Tempered Logistic Loss Based on Bregman Divergences. https://arxiv.org/pdf/1906.03361.pdf
https://google.github.io/bi-tempered-loss/
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How to calculate "simple integration" in Chapter 3 #10

Closed hihunjin closed 3 years ago

hihunjin commented 3 years ago

image This image is from your paper. You said "Via simple integration, ...". I did it by myself but the constant term $\frac{1}{2-t}$ is ambiguous. How did you get this term? What constraint did you apply?

eamid commented 3 years ago

We set the constant such that the limit t -> 2 exists and gives:

F_2(y) = sum_i (y_i - log y_i - 1)

This convex function induces the Itakura-Saito (aka Burg) divergence.