Model information metric based on selection criterion

A new criterion, named the residue Gaussianity criterion (RGC), for model selection is presented which synthetically considers the model fidelity, parameter sparsity and residue kurtosis. Here, the Gaussianity of residue is measured by its kurtosis. According to the simple idea that the whole system comprises model information and residue information after modeling the data, a metric of model information is developed. Subsequently, its reasonability is demonstrated and the relation between approximation speed and model information is discussed theoretically. Finally, several contrasting results are demonstrated about the new model information metric originating from the RGC criterion.