Submodular Kernels for Efficient Rankings

Many algorithms for ranked data become computationally intractable as the number of objects grows due to complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the preference is only known for a subset of all objects. For these reasons, state-of-the-art methods cannot scale to real-world applications, such as recommender systems. We address this challenge by exploiting geometric structure of ranked data and additional available information about the objects to derive a submodular kernel for ranking. The submodular kernel combines the efficiency of submodular optimization with the theoretical properties of kernel-based methods. We demonstrate that the submodular kernel drastically reduces the computational cost compared to state-of-the-art kernels and scales well to large datasets while attaining good empirical performance.