Fast Kronecker product kernel methods via generalized vec trick

TL;DR

This paper introduces a generalized and efficient framework for training Kronecker product kernel methods on non-complete graphs, significantly speeding up computations while maintaining high accuracy in applications like drug-target interaction prediction.

Contribution

It extends the vec trick to non-complete graphs, enabling faster training of Kronecker kernel methods for zero-shot learning scenarios.

Findings

Order of magnitude faster training and prediction times.

High accuracy maintained with the generalized approach.

Effective in applications like drug-target interaction prediction.

Abstract

Kronecker product kernel provides the standard approach in the kernel methods literature for learning from graph data, where edges are labeled and both start and end vertices have their own feature representations. The methods allow generalization to such new edges, whose start and end vertices do not appear in the training data, a setting known as zero-shot or zero-data learning. Such a setting occurs in numerous applications, including drug-target interaction prediction, collaborative filtering and information retrieval. Efficient training algorithms based on the so-called vec trick, that makes use of the special structure of the Kronecker product, are known for the case where the training data is a complete bipartite graph. In this work we generalize these results to non-complete training graphs. This allows us to derive a general framework for training Kronecker product kernel methods, as specific examples we implement Kronecker ridge regression and support vector machine algorithms. Experimental results demonstrate that the proposed approach leads to accurate models, while allowing order of magnitude improvements in training and prediction time.