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Variable stars with well-calibrated period-luminosity relationships provideaccurate distance measurements to nearby galaxies and are therefore a vitaltool for cosmology and astrophysics. While these measurements typically rely onsamples of Cepheid and RR-Lyrae stars, abundant populations of luminousvariable stars with longer periods of $10 - 1000$ days remain largely unused.We apply machine learning to derive a mapping between lightcurve features ofthese variable stars and their magnitude to extend the traditionalperiod-luminosity (PL) relation commonly used for Cepheid samples. Usingphotometric data for long period variable stars in the Large Magellanic cloud(LMC), we demonstrate that our predictions produce residual errors comparableto those obtained on the corresponding Cepheid population. We show that ourmodel generalizes well to other samples by performing a blind test onphotometric data from the Small Magellanic Cloud (SMC). Our predictions on theSMC again show small residual errors and biases, comparable to results thatemploy PL relations fitted on Cepheid samples. The residual biases arecomplementary between the long period variable and Cepheid fits, which providesexciting prospects to better control sources of systematic error incosmological distance measurements. We finally show that the proposedmethodology can be used to optimize samples of variable stars as standardcandles independent of any prior variable star classification.

Calibrating Long Period Variables as Standard Candles with Machine Learning