A Geometrical Interpretation of Exponentially Embedded Families of Gaussian Probability Density Functions for Model Selection

Model selection via exponentially embedded families (EEF) of probability models has been shown to perform well on many practical problems of interest. A key component in utilizing this approach is the definition of a model origin (i.e. null hypothesis) which is embedded individually within each competing model. In this correspondence we give a geometrical interpretation of the EEF and study the sensitivity of the EEF approach to the choice of model origin in a Gaussian hypothesis testing framework. We introduce the information center (I-center) of competing models as an origin in this procedure and compare this to using the standard null hypothesis. Finally we derive optimality conditions for which the EEF using I-center achieves optimal performance in the Gaussian hypothesis testing framework.