DiscriminativetrainingforhiddenMarkovmodels(HMMs)hasbeenacentralthemeinspeechrecognitionresearchformanyyears.Onemostpopulartechniqueisminimumclassi?cationerror(MCE)training,withtheobjectivefunctioncloselyrelatedtotheempiricalerrorrateandwiththeoptimizationmethodbasedtraditionallyongradientdescent.Inthispaper,weprovideanewlookattheMC