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 NN. The method is applied to 58 714 galaxies in CFHTLenS that have spectroscopic redshifts from DEEP2, VVDS and VIPERS. Using this data, we show that the stacked PDFs 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((zphot)) instead of N((ztruth)) is <= 1 per cent on the lensing power spectrum (P-k) 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 NN 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.