F-divergences

Let $\mathbb{X}$ be the data distribution and ${\mathcal{G}}_{\theta }(\mathcal{K})$ the generator's distribution, absolutely continuous with respect to $\mathbb{X}$. For a convex function $f:(0,\infty )\to \mathbb{R}$, strictly convex at 1 with $f(1)=0$, the f-divergence is:

F-divergences are ratio-based: they compare the two densities point by point through their ratio. KL and JS are the best-known examples; Pearson χ², Neyman χ², total variation and Hellinger come from other choices of f.