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About this paper
Ting-Kam Leonard Wong
This work introduces a new family of L^(±α)-divergences, unifying Bregman, L-divergence, and Rényi divergences within a framework based on optimal transport with a logarithmic cost function. It establishes these divergences as canonical for dually projectively flat statistical manifolds exhibiting constant curvature ∓α.
Key insights
- The introduced L^(±α)-divergences naturally interpolate between Bregman divergence and the earlier L-divergence, revealing a deeper continuum among these measures.
- Rényi divergences acquire a novel geometric interpretation, directly corresponding to L^(±α)-divergences derived from generalized exponential families.
- Optimal transport problems, when based on logarithmic cost functions, yield a class of dually projectively flat statistical manifolds with constant curvature.
Summary by alphaXiv.
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