Return of the features. Efficient feature selection and interpretation for photometric redshifts.

The explosion of data in the recent years generated an increasing need of new analysis techniques in order to extract knowledge from massive data-sets. Machine learning proved particularly useful for this task. Fully automatized methods, able to extract thousands of features from data, have recently gathered popularity, even though those methods are often lacking physical interpretability. In contrast, feature based approaches can provide both, well performing models as well as understandable causalities with respect to the correlations between features and physical processes. Efficient feature selection is an essential tool to boost the performance of machine learning models. We propose a forward selection method to compute, evaluate and characterize better performing features. Given the importance of photometric redshift estimation, we adopt it as our use case. We synthetically created 4,520 features, by combining magnitudes, errors, radii and ellipticities of quasars, taken from the 7th and 9th data release of the Sloan Digital Sky Survey (SDSS). We apply a forward selection process, a recursive method in which a huge number of feature sets is tested through a k-Nearest-Neighbors (kNN) algorithm, leading to a tree of feature sets. The branches of the feature tree are then used to perform experiments by using a random forest (RF), in order to validate the best set with an alternative model. We demonstrate that the sets of features determined with our approach improve the performances of the regression models significantly when compared to the performance of the classic features from the literature. In addition, a method to interpret the found features in a physical context is presented. The feature selection methodology described here is very general and can be used to improve the performance of machine learning models for any regression or classification task.