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Edward Kim, 01/10/2014 11:55 AM


Trees for Photo-Z

Introduction

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.

Initial Test

In this initial test, we illustrate the capabilities of TPZ by using the following set of attributes:

  • mag_model in 5 bands
  • mag_psf in 5 bands

and their respective errors. We build 100 trees by using 10 different sets of 4 random attributes, each with 10 different random attribute perturbations. The 100 trees votes to create a probabilistic classfication—if 96 trees vote galaxy and the remaining 4 vote star, we have a galaxy at 96% probability.

For training, we require that mag_model and mag_psf be less than 99.