PAC-Bayes & Margins

There are two mathematical flavors of margin bound dependent upon the weights Wi of the vote and the features Xi that the vote is taken over. The results here are of the "bll2" form. We improve on Shawe-Taylor et al. [12] and Bartlett [1] by a log(m)2 sample complexity factor and much tighter constants (1000 or unstated versus 9 or 18 as suggested by Section 2.2). In addition, the bound here covers margin errors without weakening the error-free case. Herbrich and Graepel [3] moved significantly towards the approach adopted in our paper, but the methodology adopted meant that their result does not scale well to high dimensional feature spaces as the bound here (and earlier results) do.