Adaptive confidence sets for matrix completion
Adaptive confidence sets for matrix completion
复制标题
用于矩阵补全的自适应置信集
DOI：
10.3150/17-bej933
复制
发表时间：
2016
期刊：
影响因子：
1.5
通讯作者：
Richard Nickl
中科院分区：
文献类型：
--
作者：
A. Carpentier;O. Klopp;Matthias Loffler;Richard Nickl
本文研究了矩阵完备化的诚实置信集和自适应置信集的存在性问题。我们考虑两种统计模型：迹回归模型和伯努利模型。在迹回归模型中，我们证明了即使在误差方差未知的情况下，也存在适应矩阵秩未知的诚实置信集。与此相反，我们证明了在伯努利模型中，诚实和自适应的信心集存在时，误差方差是已知的先验。在我们的证明过程中，我们得到了一些复合假设检验问题中出现的低秩推理的极大极小率的界。
In the present paper we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.