Photometric Redshift Estimation of Quasars: Local versus Global Regression

The task of estimating an object's redshift based on photometric data is one of the most important ones in astronomy. This is especially the case for quasars. Common approaches for this regression task are based on nearest neighbor search, template fitting schemes, or combinations of, e.g., clustering and regression techniques. As we show in this work, simple frameworks like k-nearest neighbor regression work extremely well if one considers the overall feature space (containing patterns of all objects with low, middle, and high redshifts). However, such methods naturally fail as soon as only very few or even no training patterns are given in the appropriate region of the feature space. In the literature, a wide range of other regression techniques can be found. Among the most popular ones are regularized regression schemes like ridge regression or support vector regression. In this work, we show that an out-of-the-box application of this type of schemes for the whole feature space is difficult due to the involved computational requirements and the specific properties of the data at hand. However, in contrast to nearest neighbor search schemes, such methods can be employed to extrapolate, i.e., they can be used to predict redshifts for patterns in new, unseen regions of the feature space.