Journal
ENTROPY
Volume 20, Issue 8, Pages -Publisher
MDPI
DOI: 10.3390/e20080575
Keywords
model selection; MDL; information geometry; von Mises-Fisher distribution; Fisher-Bingham distribution; Fisher information; Laplace approximation; Jeffreys prior
Categories
Funding
- National Science Foundation (NSF) [1263011, 1560345, IIS-1743050]
- Division Of Computer and Network Systems
- Direct For Computer & Info Scie & Enginr [1560345] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1263011] Funding Source: National Science Foundation
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We consider the problem of model selection using the Minimum Description Length (MDL) criterion for distributions with parameters on the hypersphere. Model selection algorithms aim to find a compromise between goodness of fit and model complexity. Variables often considered for complexity penalties involve number of parameters, sample size and shape of the parameter space, with the penalty term often referred to as stochastic complexity. Current model selection criteria either ignore the shape of the parameter space or incorrectly penalize the complexity of the model, largely because typical Laplace approximation techniques yield inaccurate results for curved spaces. We demonstrate how the use of a constrained Laplace approximation on the hypersphere yields a novel complexity measure that more accurately reflects the geometry of these spherical parameters spaces. We refer to this modified model selection criterion as spherical MDL. As proof of concept, spherical MDL is used for bin selection in histogram density estimation, performing favorably against other model selection criteria.
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