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Creators/Authors contains: "Qiong Wu, Felix Ming"

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  1. (, Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020)
    We study the low rank regression problem $$\my = M\mx + \epsilon$$, where $$\mx$$ and $$\my$$ are d1 and d2 dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations n is less than d1+d2. Existing algorithms are designed for settings where n is typically as large as $$\Rank(M)(d_1+d_2)$$. This work provides an efficient algorithm which only involves two SVD, and establishes statistical guarantees on its performance. The algorithm decouples the problem by first estimating the precision matrix of the features, and then solving the matrix denoising problem. To complement the upper bound, we introduce new techniques for establishing lower bounds on the performance of any algorithm for this problem. Our preliminary experiments confirm that our algorithm often out-performs existing baselines, and is always at least competitive. 
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