Computationally Efficient Sufficient Dimension Reduction via Squared-Loss Mutual Information


M. Yamada, G. Niu, J. Takagi, M. Sugiyama ;
Proceedings of the Asian Conference on Machine Learning, PMLR 20:247-262, 2011.


The purpose of sufficient dimension reduction (SDR) is to find a low-dimensional expression of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing methods. In our method, a solution is computed by iteratively performing dependence estimation and maximization: Dependence estimation is analytically carried out by recently-proposed least-squares mutual information (LSMI), and dependence maximization is also analytically carried out by utilizing the Epanechnikov kernel. Through large-scale experiments on real-world image classification and audio tagging problems, the proposed method is shown to compare favorably with existing dimension reduction approaches.

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