Beyond the Signs: Nonparametric Tensor Completion via Sign Series-猫眼课题宝

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发表时间：

2021-01

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ArXiv

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其他

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作者：

Chanwoo Lee;Miaoyan Wang

我们考虑的问题，张量估计噪声观测可能丢失的条目。基于一个新的模型，我们硬币作为符号表示张量的张量完成的非参数方法。该模型使用一系列结构化符号张量表示感兴趣的信号张量。与早期的方法不同，符号序列表示有效地解决了低秩和高秩信号，同时包含许多现有的张量模型-包括CP模型，Tucker模型，单索引模型，几个超图子模型-作为特殊情况。我们表明，符号张量系列的理论特征，计算估计，通过分类任务，仔细指定的权重。建立了超额风险界限、估计误差率和样本复杂度。我们在两个数据集上证明了我们的方法优于以前的方法，一个是人脑连接网络，另一个是主题数据挖掘。

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model represents the signal tensor of interest using a series of structured sign tensors. Unlike earlier methods, the sign series representation effectively addresses both low- and high-rank signals, while encompassing many existing tensor models -- including CP models, Tucker models, single index models, several hypergraphon models -- as special cases. We show that the sign tensor series is theoretically characterized, and computationally estimable, via classification tasks with carefully-specified weights. Excess risk bounds, estimation error rates, and sample complexities are established. We demonstrate the outperformance of our approach over previous methods on two datasets, one on human brain connectivity networks and the other on topic data mining.

Beyond the Signs: Nonparametric Tensor Completion via Sign Series

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