MADE: A spectroscopic Mass, Age, and Distance Estimator for red giant
  stars with Bayesian machine learning
  We present a new approach (MADE) that generates mass, age, and distance
estimates of red giant stars from a combination of astrometric, photometric,
and spectroscopic data. The core of the approach is a Bayesian artificial
neural network (ANN) that learns from and completely replaces stellar
isochrones. The ANN is trained using a sample of red giant stars with mass
estimates from asteroseismology. A Bayesian isochrone pipeline uses the
astrometric, photometric, spectroscopic, and asteroseismology data to determine
posterior distributions for the training outputs: mass, age, and distance.
Given new inputs, posterior predictive distributions for the outputs are
computed, taking into account both input uncertainties, and uncertainties in
the ANN parameters.
  We apply MADE to $\sim10\,000$ red giants in the overlap between the
14$^{\mathrm{th}}$ data release from the APO Galactic Evolution Experiment
(APOGEE, Abolfathi et al. 2018) and the Tycho-Gaia astrometric solution (TGAS,
Michalik et al. 2015). The ANN is able to reduce the uncertainty on mass, age,
and distance estimates for training-set stars with high output uncertainties
allocated through the Bayesian isochrone pipeline. The fractional uncertainties
on mass are $<10\%$ and on age are between $10$ to $25\%$. Moreover, the time
taken for our ANN to predict masses, ages, and distances for the entire
catalogue of APOGEE-TGAS stars is of a similar order of the time taken by the
Bayesian isochrone pipeline to run on a handful of stars. Our resulting
catalogue clearly demonstrates the expected thick and thin disc components in
the [M/H]-[$\alpha$/M] plane, when examined by age.
