Fundamental Parameters of ∼30,000 M dwarfs in LAMOST DR1 Using Data-driven Spectral Modeling

M dwarfs are the most common type of star in the Galaxy, and because of their small size are favored targets for searches of Earth-sized transiting exoplanets. Current and upcoming all-sky spectroscopic surveys, such as the Large Sky Area Multi Fiber Spectroscopic Telescope (LAMOST), offer an opportunity to systematically determine physical properties of many more M dwarfs than has been previously possible. Here, we present new effective temperatures, radii, masses, and luminosities for 29,678 M dwarfs with spectral types M0-M6 in the first data release (DR1) of LAMOST. We derived these parameters from the supervised machine-learning code, The Cannon, trained with 1388 M dwarfs in the Transiting Exoplanet Survey Satellite Cool Dwarf Catalog that were also present in LAMOST with high signal-to-noise ratio (>250) spectra. Our validation tests show that the output parameter uncertainties are strongly correlated with the signal-to-noise of the LAMOST spectra, and we achieve typical uncertainties of 110 K in T_eff (∼3%), 0.065 R⊙ (∼14%) in radius, 0.054 M⊙ (∼12%) in mass, and 0.012 ⊙ (∼20%) in luminosity. The model presented here can be rapidly applied to future LAMOST data releases, significantly extending the samples of well-characterized M dwarfs across the sky using new and exclusively data-based modeling methods.