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A note on the quasiconvex Jensen divergences and the quasiconvex Bregman divergences derived thereof [article]

Frank Nielsen, Gaëtan Hadjeres
2019 arXiv   pre-print
We then define the strictly quasiconvex Bregman divergences as the limit case of scaled and skewed quasiconvex Jensen divergences, and report a simple closed-form formula which shows that these divergences  ...  To remedy this problem, we propose the δ-averaged quasiconvex Bregman divergences which integrate the pseudo-divergences over a small neighborhood in order obtain a proper divergence.  ...  We summarize our main contributions as follows: • By using quasiconvex generators instead of convex generators, we define the skewed quasiconvex Jensen divergences (Definition 1) and derived thereof quasiconvex  ... 
arXiv:1909.08857v2 fatcat:wxupexjq4jayjdyukd5nvi3fpe