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.
