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Dynamic Partial Sufficient Dimension Reduction
Sufficient dimension reduction aims for reduction of dimensionality of a...
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Continuum directions for supervised dimension reduction
Dimension reduction of multivariate data supervised by auxiliary informa...
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On sufficient dimension reduction via principal asymmetric least squares
In this paper, we introduce principal asymmetric least squares (PALS) as...
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Distributed estimation of principal support vector machines for sufficient dimension reduction
The principal support vector machines method (Li et al., 2011) is a powe...
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Sufficient Dimension Reduction for Classification
We propose a new sufficient dimension reduction approach designed delibe...
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Unsupervised Bump Hunting Using Principal Components
Principal Components Analysis is a widely used technique for dimension r...
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Sufficient Component Analysis for Supervised Dimension Reduction
The purpose of sufficient dimension reduction (SDR) is to find the low-d...
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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.
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