Using neural networks to estimate redshift distributions. An application to CFHTLenS

We present a novel way of using neural networks (NN) to estimate the redshift distribution of a galaxy sample. We are able to obtain a probability density function (PDF) for each galaxy using a classification neural network. The method is applied to 58714 galaxies in CFHTLenS that have spectroscopic redshifts from DEEP2, VVDS and VIPERS. Using this data we show that the stacked PDF's give an excellent representation of the true $N(z)$ using information from 5, 4 or 3 photometric bands. We show that the fractional error due to using N(z_(phot)) instead of N(z_(truth)) is <=1 on the lensing power spectrum P_(kappa) in several tomographic bins. Further we investigate how well this method performs when few training samples are available and show that in this regime the neural network slightly overestimates the N(z) at high z. Finally the case where the training sample is not representative of the full data set is investigated. An IPython notebook accompanying this paper is made available here: https://bitbucket.org/christopher_bonnett/nn_notebook