Spectrophotometric parallaxes with linear models: Accurate distances for
  luminous red-giant stars
  With contemporary infrared spectroscopic surveys like APOGEE, red-giant stars
can be observed to distances and extinctions at which Gaia parallaxes are not
highly informative. Yet the combination of effective temperature, surface
gravity, composition, and age - all accessible through spectroscopy -
determines a giant's luminosity. Therefore spectroscopy plus photometry should
enable precise spectrophotometric distance estimates. Here we use the
APOGEE-Gaia-2MASS-WISE overlap to train a data-driven model to predict
parallaxes for red-giant branch stars with $0<\log g\leq2.2$ (more luminous
than the red clump). We employ (the exponentiation of) a linear function of
APOGEE spectral pixel intensities and multi-band photometry to predict parallax
spectrophotometrically. The model training involves no logarithms or inverses
of the Gaia parallaxes, and needs no cut on the Gaia parallax signal-to-noise
ratio. It includes an L1 regularization to zero out the contributions of
uninformative pixels. The training is performed with leave-out subsamples such
that no star's astrometry is used even indirectly in its spectrophotometric
parallax estimate. The model implicitly performs a reddening and extinction
correction in its parallax prediction, without any explicit dust model. We
assign to each star in the sample a new spectrophotometric parallax estimate;
these parallaxes have uncertainties of a few to 15 percent, depending on data
quality, which is more precise than the Gaia parallax for the vast majority of
targets, and certainly any stars more than a few kpc distance. We obtain
10-percent distance estimates out to heliocentric distances of $20\,$kpc, and
make global maps of the Milky Way's disk.
