Poisson matrix completion
Poisson matrix completion
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泊松矩阵完成
DOI：
10.1109/isit.2015.7282774
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Yao Xie
中科院分区：
文献类型：
--
作者：
Yang Cao;Yao Xie
我们将矩阵完备化理论推广到对低秩矩阵项的子集进行泊松观测的情况。我们考虑(现在)通常的矩阵恢复公式，通过对大小为D_1×D_2的矩阵M进行适当约束的极大似然估计，建立了恢复误差的理论上界和下界。我们的界几乎是最优的，直到O(log(D1d2))的阶因子。这些界限是通过适应用于一位矩阵补全[1]的自变量[1](尽管这两个问题本质上不同)而获得的，并且这种适应需要利用泊松似然函数的性质和解决泊松分布的局部亚高斯特性所带来的困难的新技术。我们的结果突出了泊松矩阵完成与以前的矩阵完成工作相比的一些重要区别，包括必须在每个观察到的条目上施加最小的信噪比要求。我们还开发了一种高效的迭代算法，并在太阳耀斑图像恢复中证明了其良好的性能。
We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix M of size d1-by-d2, and establish theoretical upper and lower bounds on the recovery error. Our bounds are nearly optimal up to a factor on the order of O(log(d1d2)). These bounds are obtained by adapting the arguments used for one-bit matrix completion [1] (although these two problems are different in nature) and the adaptation requires new techniques exploiting properties of the Poisson likelihood function and tackling the difficulties posed by the locally sub-Gaussian characteristic of the Poisson distribution. Our results highlight a few important distinctions of Poisson matrix completion compared to the prior work in matrix completion including having to impose a minimum signal-to-noise requirement on each observed entry. We also develop an efficient iterative algorithm and demonstrate its good performance in recovering solar flare images.