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Abstract:
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We study the problem of envelope estimation, a dimension reduction method for multivariate linear regression. Envelope estimation requires minimizing a function over the Grassman manifold, and obtaining envelopes can be numerically very costly. We extend the alternating directions method of multipliers to Grassman manifolds. This gives rise to a new algorithm for envelope estimation in which PCA is applied successively to a set of matrices until the eigenspaces of these matrices overlap. We present results on the convergence of the algorithm. We show how the algorithm can be adapted to perform dimension reduction in other multivariate problems, and propose subsampling-based extensions for large datasets.
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