Is celebrating the birth of the Prophet a form of innovation?

Is celebrating Mawalid (birth of the Prophet) bidat (innovation)? Please note this question is different of "if Mawalid is Halal or Haram" because one action can be bidat but still halal. Or it might be not be bidat, but still haram. *Please mention the reasoning for your answer from Quran or authentic hadith and not only a fitwa.*