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- W4289376674 abstract "We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex optimization problem, which is then solved using the alternating direction method of multipliers algorithm. We establish non-asymptotic estimation error bounds under both Frobenius and nuclear norms in the high-dimensional setting. This is a major contribution over existing results in reduced rank regression, which mainly focus on rank selection and prediction consistency. Our theoretical results quantify the tradeoff between heavy-tailedness of the random noise and statistical bias. For random noise with bounded $(1+delta)$th moment with $delta in (0,1)$, the rate of convergence is a function of $delta$, and is slower than the sub-Gaussian-type deviation bounds; for random noise with bounded second moment, we obtain a rate of convergence as if sub-Gaussian noise were assumed. Furthermore, the transition between the two regimes is smooth. We illustrate the performance of the proposed method via extensive numerical studies and a data application." @default.
- W4289376674 created "2022-08-02" @default.
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- W4289376674 date "2018-10-18" @default.
- W4289376674 modified "2023-10-01" @default.
- W4289376674 title "Robust Sparse Reduced Rank Regression in High Dimensions" @default.
- W4289376674 doi "https://doi.org/10.48550/arxiv.1810.07913" @default.
- W4289376674 hasPublicationYear "2018" @default.
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