Mixture models for photometric redshifts

Determining photometric redshifts to high accuracy is paramount to measure distances in wide-field cosmological experiments. With only photometric information at hand, photo-zs are prone to systematic uncertainties in the intervening extinction and the unknown underlying spectral-energy distribution of different astrophysical sources. Here, we aim to resolve these model degeneracies and obtain a clear separation between intrinsic physical properties of astrophysical sources and extrinsic systematics. We aim at estimates of the full photo-z probability distributions, and their uncertainties. We perform a probabilistic photo-z determination using Mixture Density Networks (MDN). The training data-set is composed of optical ($griz$) point-spread-function and model magnitudes and extinction measurements from the SDSS-DR15, and WISE midinfrared ($3.4 \mu$m and $4.6 \mu$m) model magnitudes. We use Infinite Gaussian Mixture models to classify the objects in our data-set as stars, galaxies or quasars, and to determine the number of MDN components to achieve optimal performance. The fraction of objects that are correctly split into the main classes is 94%. Our method improves the bias of photometric redshift estimation (i.e. the mean $\Delta z$ = (zp - zs)/(1 + zs)) by one order of magnitude compared to the SDSS photo-z, and decreases the fraction of $3 \sigma$ outliers (i.e. 3rms$(\Delta z) < \Delta z$). The relative, root-mean-square systematic uncertainty in our resulting photo-zs is down to 1.7% for low-redshift galaxies (zs $<$ 0.5). We have demonstrated the feasibility of machine-learning based methods that produce full probability distributions for photo-z estimates with a performance that is competitive with state-of-the art techniques. Our method can be applied to wide-field surveys where extinction can vary significantly across the sky and with sparse spectroscopic calibration samples.