## JMI2009B-3 Bregman divergence and density integration (pp.97-104)

Author(s)： Noboru Murata and Yu Fujimoto

J. Math-for-Ind. 1B (2009) 97-104.

Abstract
In this paper, a problem of integrating density functions is considered. First, the Bregman divergence in the space of positive finite measures is introduced, and properties of consistent subspaces and well-behaved parametric models associated with the Bregman divergence is investigated. Based on those results, a natural method for integration of estimates from the Bregman divergence is derived.

Keyword(s).　 Bregman divergence, consistent subspace, Pythagorean relation, $u$-model, density integration