1 research outputs found
Sufficient dimension reduction for classification using principal optimal transport direction
Sufficient dimension reduction is used pervasively as a supervised dimension
reduction approach. Most existing sufficient dimension reduction methods are
developed for data with a continuous response and may have an unsatisfactory
performance for the categorical response, especially for the binary-response.
To address this issue, we propose a novel estimation method of sufficient
dimension reduction subspace (SDR subspace) using optimal transport. The
proposed method, named principal optimal transport direction (POTD), estimates
the basis of the SDR subspace using the principal directions of the optimal
transport coupling between the data respecting different response categories.
The proposed method also reveals the relationship among three seemingly
irrelevant topics, i.e., sufficient dimension reduction, support vector
machine, and optimal transport. We study the asymptotic properties of POTD and
show that in the cases when the class labels contain no error, POTD estimates
the SDR subspace exclusively. Empirical studies show POTD outperforms most of
the state-of-the-art linear dimension reduction methods.Comment: 18 pages, 4 figures, to be published in 34th Conference on Neural
Information Processing Systems (NeurIPS 2020), add the supplementary materia