Nonparametric Matrix Estimation with One-Sided Covariates
Nonparametric Matrix Estimation with One-Sided Covariates
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DOI：
10.1109/isit50566.2022.9834608
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
C. Yu
中科院分区：
文献类型：
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作者：
C. Yu
考虑矩阵估计的任务，在该任务中，我们希望在给定稀疏和噪声观测的情况下估计地面真实矩阵。以概率p独立地观察到每个条目，并且附加地受到附加观测噪声的干扰。假设基本真值矩阵的第(u，i)项对于某个Holder光滑函数f可以用f(αu，βi)来描述。我们考虑这样的设置，其中行协变量α未被观测而列协变量β被观测。我们给出了一个算法，并进行了分析，结果表明，在行数不太少的情况下，我们的算法改进了单纯地分别估计每一行的方法。此外，当矩阵比例适中时，我们的算法达到了知道行协变量的Oracle算法的极小极大最优非参数比率。在模拟实验中，我们证明了我们的算法在低数据区域的性能优于其他基线。
Consider the task of matrix estimation, in which we desire to estimate a ground truth matrix given sparse and noisy observations. Each entry is observed independently with probability p, and additionally perturbed with additive observation noise. Assume the (u,i)-th entry of the ground truth matrix can be described by f(αu,βi) for some Holder smooth function f. We consider the setting where the row covariates α are unobserved yet the column covariates β are observed. We provide an algorithm and accompanying analysis which shows that our algorithm improves upon naively estimating each row separately when the number of rows is not too small. Furthermore when the matrix is moderately proportioned, our algorithm achieves the minimax optimal nonparametric rate of an oracle algorithm that knows the row covariates. In simulated experiments we show our algorithm outperforms other baselines in low data regimes.