The statistical minkowski distances: Closed-form formula for Gaussian mixture models

Author

Nielsen, Frank

Abstract

The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose statistical symmetric distances based on the Minkowski’s inequality for probability densities belonging to Lebesgue spaces. These statistical Minkowski distances admit closed-form formula for Gaussian mixture models when parameterized by integer exponents.