It is well known that the total variation is a distance, whereas the KL-divergence is not. I am wondering under what conditions on $f$, the induced $f$-divergence is a distance? Or consider a weaker proposition, when will $f$-divergence satisfy the triangle inequality?
2026-04-02 20:55:35.1775163335
Under what conditions is the $f$-divergence a distance?
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