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  1. Free, publicly-accessible full text available December 7, 2022
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  5. 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 newmore »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.« less
  6. Efficient construction of checkpoints/snapshots is a critical tool for training and diagnosing deep learning models. In this paper, we propose a lossy compression scheme for checkpoint constructions (called LC-Checkpoint). LC-Checkpoint simultaneously maximizes the compression rate and optimizes the recovery speed, under the assumption that SGD is used to train the model. LC-Checkpointuses quantization and priority promotion to store the most crucial information for SGD to recover, and then uses a Huffman coding to leverage the non-uniform distribution of the gradient scales. Our extensive experiments show that LC-Checkpoint achieves a compression rate up to 28× and recovery speedup up to 5.77×more »over a state-of-the-art algorithm (SCAR).« less