How to measure metallicity from five-band photometry with supervised
  machine learning algorithms
  We demonstrate that it is possible to measure metallicity from the SDSS
five-band photometry to better than 0.1 dex using supervised machine learning
algorithms. Using spectroscopic estimates of metallicity as ground truth, we
build, optimize and train several estimators to predict metallicity. We use the
observed photometry, as well as derived quantities such as stellar mass and
photometric redshift, as features, and we build two sample data sets at median
redshifts of 0.103 and 0.218 and median r-band magnitude of 17.5 and 18.3
respectively. We find that ensemble methods, such as Random Forests of Trees
and Extremely Randomized Trees, and Support Vector Machines all perform
comparably well and can measure metallicity with a Root Mean Square Error
(RMSE) of 0.081 and 0.090 for the two data sets when all objects are included.
The fraction of outliers (objects for which |Z_true - Z_pred| > 0.2 dex) is 2.2
and 3.9%, respectively and the RMSE decreases to 0.068 and 0.069 if those
objects are excluded. Because of the ability of these algorithms to capture
complex relationships between data and target, our technique performs better
than previously proposed methods that sought to fit metallicity using an
analytic fitting formula, and has 3x more constraining power than SED
fitting-based methods. Additionally, this method is extremely forgiving of
contamination in the training set, and can be used with very satisfactory
results for training sample sizes of just a few hundred objects. We distribute
all the routines to reproduce our results and apply them to other data sets.
