The base scoring functions used in our algorithm have the form In particular, these can be derived from the path experts in H by letting h k t (x, y) = 1 h k t (x)=y k .
the score assigned to y by the base scoring function h t is the number of positions at which y matches the prediction of path expert h t given input x. H Boost is defined as follows in terms of h or h t s: We remark that the analysis and algorithm presented in this section are also applicable with a scoring function that is the product of the scores at each substructure k as opposed to a sum, that is, This can be used for example in the case where the experts are derived from probabilistic models.