论文标题
信号检测的功能重新归一化组方法
Functional Renormalization Group Approach for Signal Detection
论文作者
论文摘要
这篇评论论文使用重新归一化的组技术在几乎连续的正谱中进行信号检测。我们重点介绍了模拟现场理论方法的普遍方面。第一个目的是介绍用于数据的有效现场理论框架的扩展自一致构造，该框架可以看作是最大熵模型。特别是利用普遍性论点，我们证明了经典行动的$ \ mathbb {z} _2 $ - 对称性，并强调存在大型（本地）制度和小型（非局部）制度的存在。其次，与噪声模型有关，我们观察到检测阈值附近的相变和对称性破裂之间的普遍关系。最后，我们讨论了定义类似于张紧数据的协方差矩阵的问题。基于切割图处方，我们根据大尺寸的完整图进行了定义的优越性，用于数据分析。
This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be viewed as a maximum entropy model. In particular and exploiting universality arguments, we justify the $\mathbb{Z}_2$-symmetry of the classical action and we stress the existence of a large-scale (local) regime and of a small-scale (nonlocal) regime. Secondly and related to noise models, we observe the universal relation between phase transition and symmetry breaking in the vicinity of the detection threshold. Finally, we discuss the issue of defining the covariance matrix for tensorial-like data. Based on the cutting graph prescription, we note the superiority of definitions based on complete graphs of large size for data analysis.
