Abstract
We developed a deep convolutional neural network (CNN), used as a classifier, to estimate photometric redshifts and associated probability distribution functions (PDF) for galaxies in the Main Galaxy Sample of the Sloan Digital Sky Survey at z < 0.4. Our method exploits all the information present in the images without any feature extraction. The input data consist of 64 × 64 pixel ugriz images centered on the spectroscopic targets, plus the galactic reddening value on the line-of-sight. For training sets of 100k objects or more (≥20% of the database), we reach a dispersion σMAD < 0.01, significantly lower than the current best one obtained from another machine learning technique on the same sample. The bias is lower than 10−4, independent of photometric redshift. The PDFs are shown to have very good predictive power. We also find that the CNN redshifts are unbiased with respect to galaxy inclination, and that σMAD decreases with the signal-to-noise ratio (S/N), achieving values below 0.007 for S/N > 100, as in the deep stacked region of Stripe 82. We argue that for most galaxies the precision is limited by the S/N of SDSS images rather than by the method. The success of this experiment at low redshift opens promising perspectives for upcoming surveys.
Highlights
Panoramic imaging surveys for cosmology are underway or in preparation phase (HSC, LSST, Euclid, WFIRST)
Another challenge is the derivation of robust redshift probability distribution functions (PDFs, Mandelbaum et al 2008) for a complete understanding of the uncertainties attached to any measurements in cosmology or galaxy evolution
We retrieved the photometric redshifts of Beck et al (2016, hereafter B16), which are the only such redshifts available for comparison in data release 12 (DR12). They were computed with a k-neural networks (NNs) method (Csabai et al 2007, local linear regression) that included five dimensions (r magnitude and u − g, g − r, r − i, i − z colors) and trained with deep and high redshift spectroscopic surveys in addition to the Sloan Digital Sky Survey (SDSS). These photometric redshifts have similar or better accuracies than those inferred from random forests or prediction trees on the Main Galaxy Sample (MGS) sample (Carrasco Kind & Brunner 2013; Carliles et al 2010), and may serve as reference for machine learning photometric redshifts based on photometric measurements
Summary
Panoramic imaging surveys for cosmology are underway or in preparation phase (HSC, LSST, Euclid, WFIRST). They were computed with a k-NN method (Csabai et al 2007, local linear regression) that included five dimensions (r magnitude and u − g, g − r, r − i, i − z colors) and trained with deep and high redshift spectroscopic surveys in addition to the SDSS These photometric redshifts have similar or better accuracies than those inferred from random forests or prediction trees on the MGS sample (Carrasco Kind & Brunner 2013; Carliles et al 2010), and may serve as reference for machine learning photometric redshifts based on photometric measurements.
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