Web: http://arxiv.org/abs/2203.02839

Sept. 19, 2022, 1:13 a.m. | Liwei Jiang, Yudong Chen, Lijun Ding

stat.ML updates on arXiv.org arxiv.org

We study the asymmetric matrix factorization problem under a natural
nonconvex formulation with arbitrary overparametrization. The model-free
setting is considered, with minimal assumption on the rank or singular values
of the observed matrix, where the global optima provably overfit. We show that
vanilla gradient descent with small random initialization sequentially recovers
the principal components of the observed matrix. Consequently, when equipped
with proper early stopping, gradient descent produces the best low-rank
approximation of the observed matrix without explicit regularization. We …

arxiv factorization free regularization

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