Generalized vec trick for fast learning of pairwise kernel models

Pairwise learning corresponds to the supervised setting where goal is make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, customer-product preferences. In this work, we present a comprehensive review pairwise kernels, that have been proposed incorporating prior knowledge about relationship between Specifically, consider standard, symmetric and anti-symmetric Kronecker product metric-learning, Cartesian, ranking, as well linear, polynomial Gaussian kernels. Recently, O(nm + nq) time generalized vec trick algorithm, n, m, q denote number pairs, drugs targets, was introduced training kernel methods with kernel. This significant improvement over previous O(n^2) methods, since in most real-world m,q << n. work show how all reviewed kernels can be expressed sums products, allowing use speeding up their computation. experiments, demonstrate approach allows scaling much larger data sets than previously feasible, provide an extensive comparison on biological interaction prediction tasks.