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Spectrophotometric distances to stars observed by large spectroscopic surveysoffer a crucial complement to parallax distances that remain very importantalso after the future Gaia data releases. Here we present a probabilisticapproach to modeling spectroscopic information for a subset of 4,000 mainsequence stars with good parallaxes ($\sigma_\varpi/\varpi<0.1$) from theLAMOST $\times$ TGAS $\times$ 2MASS cross-match, yielding a precisespectroscopic distance estimator with uncertainties of $\sim$6% for singlestars. Unlike previous approaches to this problem, we explicitly account forthe individual parallax uncertainties in the model building and fullyincorporate the fraction of near-equal binaries of main sequence stars, whichwould lead to biased distance estimates if neglected. Using this model, weestimate the distance for all (150,000) main sequence stars from LAMOST DataRelease 5, without parallax information. As an application, we compute theirorbital actions, where our more precise distances result in 5 times smalleraction uncertainties. This illustrates how future studies of the Milky Way'sorbital structure can benefit from using our model. For the fainter and moredistant stars of most current spectroscopic surveys, an approach such as theone presented in this work will deliver better distances than Gaia Data Release2.

Unbiased TGAS$\times$LAMOST distances and the role of binarity