Trees for Photo-Z¶
Trees for Photo-Z (TPZ) is a supervised machine learning, parallel algorithm that uses prediction trees and random forest techniques to produce both robust photometric redshift PDFs and ancillary information for a galaxy sample. A prediction tree is built by asking a sequence of questions that recursively split the input data taken from the spectroscopic sample, frequently into two branches, until a terminal leaf is created that meets a stopping criterion (e.g., a minimum leaf size or a variance threshold). The dimension in which the data is divided is chosen to be the one with highest information gain among the random subsample of dimensions obtained at every point. This process produces less correlated trees and allows to explore several configurations within the data. The small region bounding the data in the terminal leaf node represents a specific subsample of the entire data with similar properties. Within this leaf, a model is applied that provides a fairly comprehensible prediction, especially in situations where many variables may exist that interact in a nonlinear manner as is often the case with photo-z estimation.
TPZ is a supervised algorithm in the framework of Machine Learning for Photo-Z (MLZ), a machine learning software package that combines all of our recent photometric redshift algorithms and implementations. MLZ also includes a unsupervised method with self organizing maps and random atlas through SOMz. For more information, refer to the Laboratory for Cosmological Data Mining website (lcdm.astro.illinois.edu) at the University of Illinois at Urbana-Champaign.
Download tpz_r1.tar.gz to see the result of running our TPZ code on the provided test_sgchallenge_r1.fits file. It is a compressed ASCII file with RA, DEC, and probabilistic separator values ranging from 0 (galaxies) to 1 (stars).
In this initial test, we illustrate the capabilities of TPZ by using the following set of attributes:
- mag_model in g, r, i, z, y bands
- mag_psf in g, r, i, z, y bands
and their respective errors. For training, we require that mag_model and mag_psf be less than 99. We build a total of 500 trees by using 10 random realizations of 4 random attributes, each with 50 trees. The 500 trees vote to create a probabilistic classfication—if 480 trees vote galaxy and the remaining 20 vote star, we have a galaxy at 96% probability.
In the figure below, we show the completeness for the sources, classified at a probability of 96% or greater, as a function of magnitude in i band. Note that we also display the confusion matrix in the lower right corner.
We also plot the Receiver Operating Characteristic (ROC) curve. The area under the curve is 0.93.
Carrasco Kind, M., & Brunner, R. J., 2013 “TPZ : Photometric redshift PDFs and ancillary information by using prediction trees and random forests”, MNRAS, 432, 1483 (link)
Carrasco Kind, M., & Brunner, R. J., 2014, “SOMz : photometric redshift PDFs with self organizing maps and random atlas” , MNRAS, in press (link)