The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models

Understand

The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces.

• In this work, we propose novel 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.
• This result extends to arbitrary mixtures of exponential families with natural parameter spaces being cones: This includes the binomial, the multinomial, the zero-centered Laplacian, the Gaussian and the Wishart mixtures, among others.