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# Magnitude-Preserving Ranking for Structured Outputs

*Proceedings of the Ninth Asian Conference on Machine Learning*, PMLR 77:407-422, 2017.

#### Abstract

In this paper, we present a novel method for solving structured prediction problems, based on combining Input Output Kernel Regression (IOKR) with an extension of magnitude-preserving ranking to structured output spaces. In particular, we concentrate on the case where a set of candidate outputs has been given, and the associated pre-image problem calls for ranking the set of candidate outputs. Our method, called magnitude-preserving IOKR, both aims to produce a good approximation of the output feature vectors, and to preserve the magnitude differences of the output features in the candidate sets. For the case where the candidate set does not contain corresponding ’correct’ inputs, we propose a method for approximating the inputs through application of IOKR in the reverse direction. We apply our method to two learning problems: cross-lingual document retrieval and metabolite identification. Experiments show that the proposed approach improves performance over IOKR, and in the latter application obtains the current state-of-the-art accuracy.