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Fundamental Parameters of $\sim$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-Object 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 1,388 M dwarfs in the Transiting Exoplanet Survey Satellite (TESS) Cool Dwarf Catalog that were also present in LAMOST with high signal-to-noise ratio ($>$250) spectra. Our validation tests show that the output parameter uncertainties are strongly correlated with the signal-to-noise of the LAMOST spectra, and we achieve typical uncertainties of 110 K in Teff ($\sim$3%), 0.065 $R_{\odot}$ ($\sim$14%) in radius, 0.054 $M_{\odot}$ ($\sim$12%) in mass, and 0.012 $L_{\odot}$ ($\sim$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.