Estimation with infinite-dimensional exponential family and Fisher divergence

Abstract

Abstract Infinite dimensional exponential families have been theoretically studied, but their practical applications are still limited because empirical estimation is not straightforward. This paper first gives a brief survey of studies on the estimation method for infinite-dimensional exponential families. The method uses score matching, which is based on the Fisher divergence. The second topic is to investigate the Fisher divergence as a member of an extended family of divergences, which employ operators in defining divergences.