On the smallest enclosing information disk

We present a generalization of Welzl's smallest enclosing disk algorithm [E. Welzl, Smallest enclosing disks (balls and ellipsoids), in: New Results and New Trends in Computer Science, in: Lecture Notes in Computer Science, vol. 555, Springer, 1991, pp. 359–370] for point sets lying in information-geometric spaces. Given a set of points equipped with a Bregman divergence as a (dis)similarity measure, we investigate the problem of finding its unique (circum)center defined as the point minimizing the maximum divergence to the point set. As an application, we show how to solve a statistical model estimation problem by computing the center of a finite set of univariate normal distributions.