On signal detection and confidence sets for low rank inference problems

Alexandra Carpentier; Richard Nickl

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On signal detection and confidence sets for low rank inference problems

机译：关于低秩推理问题的信号检测和置信集

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We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal.

机译：我们在具有低秩替代假设的高斯设计迹线回归模型中考虑信号检测问题。我们推导了Frobenius和核规范的精确（英格斯特型）检测边界。然后，我们将这些结果应用于表明，不存在适用于核规范中所有低秩子模型的未知矩阵参数的诚实置信集。这表明，最近在[5]中针对低等级恢复问题的置信度集获得的积极结果基本上是最佳的。

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《Electronic Journal of Statistics》 |2015年第2期|共14页
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Alexandra Carpentier; Richard Nickl;
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中图分类统计学;
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1. Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases [J] . Bickel David R. Communications in Statistics . 2017,第21a22期

机译：置信分布用于基于估计局部错误发现率将不确定性传播到推理：随着比较次数的增加，从置信集到经验贝叶斯集的基准连续性估计
2. Confidence factor weighted Gaussian function induced parallel fuzzy rank-level fusion for inference and its application to face recognition [J] . Sing Jamuna Kanta, Dey Aniruddha, Ghosh Manas Information Fusion . 2019,第期

机译：置信因子加权高斯函数诱导平行模糊秩级融合的推论及其应用于面对识别
3. Low-rank detection of multichannel Gaussian signals using block matrix approximation [J] . Strobach P. IEEE Transactions on Signal Processing . 1995,第1期

机译：使用块矩阵逼近对多通道高斯信号进行低秩检测
4. Adaptive Detection of Structured Signals in Low-Rank Interference [C] . Philip Schniter, Evan Byrne 2018 52nd Asilomar Conference on Signals, Systems, and Computers . 2018

机译：低秩干扰中结构化信号的自适应检测
5. Detection of low rank signals in noise and fast correlation mining with applications to large biological data. [D] . Shabalin, Andrey A. 2010

机译：噪声中低秩信号的检测以及快速关联挖掘以及对大型生物数据的应用。
6. Optimal structural inference of signaling pathways from unordered and overlapping gene sets [O] . Lipi R. Acharya, Thair Judeh, Guangdi Wang, -1

机译：来自无序和重叠基因集的信号通路的最佳结构推断
7. On signal detection and confidence sets for low rank inference problems [O] . Carpentier, Alexandra, Nickl, Richard 2015

机译：关于低秩推理问题的信号检测和置信集
8. Confidence Set Inference with a Prior Quadratic Bound [R] . Backus, G. E. 1989

机译：具有先验二次边界的置信集推断

On signal detection and confidence sets for low rank inference problems

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