Accurate determination of stellar atmospheric parameters and elemental abundances is crucial for Galactic archeology via large-scale spectroscopic surveys . In this paper , we estimate stellar atmospheric parameters — effective temperature T _ { eff } , surface gravity log g and metallicity [ Fe/H ] , absolute magnitudes { M } _ { V } and { M } _ { K { s } } , \alpha -element to metal ( and iron ) abundance ratio [ \alpha /M ] ( and [ \alpha /Fe ] ) , as well as carbon and nitrogen abundances [ C/H ] and [ N/H ] from the LAMOST spectra with a multivariate regression method based on kernel-based principal component analysis , using stars in common with other surveys ( Hipparcos , Kepler , APOGEE ) as training data sets . Both internal and external examinations indicate that given a spectral signal-to-noise ratio ( SNR ) better than 50 , our method is capable of delivering stellar parameters with a precision of \sim 100 K for T _ { eff } , \sim 0.1 dex for log g , 0.3 – 0.4 mag for { M } _ { V } and { M } _ { K { s } } , 0.1 dex for [ Fe/H ] , [ C/H ] and [ N/H ] , and better than 0.05 dex for [ \alpha /M ] ( [ \alpha /Fe ] ) . The results are satisfactory even for a spectral SNR of 20 . The work presents first determinations of [ C/H ] and [ N/H ] abundances from a vast data set of LAMOST , and , to our knowledge , the first reported implementation of absolute magnitude estimation directly based on the observed spectra . The derived stellar parameters for millions of stars from the LAMOST surveys will be publicly available in the form of value-added catalogues .