Calibrating Long Period Variables as Standard Candles with Machine
  Learning
  Variable stars with well-calibrated period-luminosity relationships provide
accurate distance measurements to nearby galaxies and are therefore a vital
tool for cosmology and astrophysics. While these measurements typically rely on
samples of Cepheid and RR-Lyrae stars, abundant populations of luminous
variable stars with longer periods of $10 - 1000$ days remain largely unused.
We apply machine learning to derive a mapping between lightcurve features of
these variable stars and their magnitude to extend the traditional
period-luminosity (PL) relation commonly used for Cepheid samples. Using
photometric data for long period variable stars in the Large Magellanic cloud
(LMC), we demonstrate that our predictions produce residual errors comparable
to those obtained on the corresponding Cepheid population. We show that our
model generalizes well to other samples by performing a blind test on
photometric data from the Small Magellanic Cloud (SMC). Our predictions on the
SMC again show small residual errors and biases, comparable to results that
employ PL relations fitted on Cepheid samples. The residual biases are
complementary between the long period variable and Cepheid fits, which provides
exciting prospects to better control sources of systematic error in
cosmological distance measurements. We finally show that the proposed
methodology can be used to optimize samples of variable stars as standard
candles independent of any prior variable star classification.
