The Gelug or Gelug-pa , is a school of Tibetan Buddhism founded by Je Tsongkhapa ( 1357 â `` 1419 ) , a philosopher and Tibetan religious leader . The Gelug or Gelug-pa ( or dGe Lugs Pa , dge-lugs-pa , or Dgelugspa ) , also known as the Yellow Hat sect , is a school of Buddhism founded by Je Tsongkhapa ( 1357 â `` 1419 ) , a philosopher and Tibetan religious leader .