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Abstract:
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In multivariate regression models, a sparse singular value decomposition of the regression component matrix is appealing for reducing dimensionality and facilitating interpretation. However, the recovery of such a decomposition remains very challenging, largely due to the simultaneous presence of orthogonality constraints and co-sparsity regularization. By delving into the underlying statistical data generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, and develop an efficient sequential computation procedure that completely bypasses the orthogonality requirements. At each sequential step, the problem reduces to a sparse multivariate regression with a unit-rank constraint. Nicely, each sequentially extracted sparse and unit-rank coefficient matrix automatically leads to co-sparsity in its pair of singular vectors. Each latent factor is thus a sparse linear combination of the predictors and may influence only a subset of responses. Our estimators enjoy the oracle properties asymptotically; a non-asymptotic error bound further reveals some interesting finite-sample behaviors of the estimators. We depict efficacy of our method through examples.
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