Variable Selection for Modeling the Absolute Magnitude at Maximum of Type Ia Supernovae

We discuss what is an appropriate set of explanatory variables in order to predict the absolute magnitude at the maximum of Type Ia supernovae. In order to have a good prediction, the error for future data, which is called the "generalization error," should be small. We use cross-validation in order to control the generalization error and LASSO-type estimator in order to choose the set of variables. This approach can be used even in the case that the number of samples is smaller than the number of candidate variables. We studied the Berkeley supernova database with our approach. Candidates of the explanatory variables include normalized spectral data, variables about lines, and previously proposed flux-ratios, as well as the color and light-curve widths. As a result, we confirmed the past understanding about Type Ia supernova: i) The absolute magnitude at maximum depends on the color and light-curve width. ii) The light-curve width depends on the strength of Si II. Recent studies have suggested to add more variables in order to explain the absolute magnitude. However, our analysis does not support to add any other variables in order to have a better generalization error.