论文标题
从压缩测量中优先恢复协方差和因果图的密度演化框架
A Density Evolution framework for Preferential Recovery of Covariance and Causal Graphs from Compressed Measurements
论文作者
论文摘要
在本文中，我们提出了一个通用框架，用于设计传感矩阵$ \ boldsymbol {a} \ in \ mathbb {r}^{d \ times p} $，用于估算从形式的稀疏协方差矩阵估算稀疏协方差矩阵， \ boldsymbol {n} $，其中$ \ boldsymbol {y}，\ boldsymbol {n} \ in \ mathbb {r}^d $和$ \ boldsymbol {x} \ in \ mathbb {r Mathbb {r}^p $。通过将协方差恢复视为因素图通过消息传递算法的推断，从\ textit {密度进化}（de）等编码理论中的想法就可以构建一个框架，以设计感应矩阵的设计。所提出的框架可以处理（1）常规感应，即对协方差的所有条目都具有同等的重要性，并且（2）优先感应，即，对协方差矩阵的一部分给出了更高的重要性。通过实验，我们表明，通过密度演化设计的传感矩阵可以与常规感测范式中的协方差恢复相匹配，并在优先传感范围内提高了性能。此外，我们使用从压缩测量值获得的估计协方差矩阵研究因果图结构恢复的可行性。
In this paper, we propose a general framework for designing sensing matrix $\boldsymbol{A} \in \mathbb{R}^{d\times p}$, for estimation of sparse covariance matrix from compressed measurements of the form $\boldsymbol{y} = \boldsymbol{A}\boldsymbol{x} + \boldsymbol{n}$, where $\boldsymbol{y}, \boldsymbol{n} \in \mathbb{R}^d$, and $\boldsymbol{x} \in \mathbb{R}^p$. By viewing covariance recovery as inference over factor graphs via message passing algorithm, ideas from coding theory, such as \textit{Density Evolution} (DE), are leveraged to construct a framework for the design of the sensing matrix. The proposed framework can handle both (1) regular sensing, i.e., equal importance is given to all entries of the covariance, and (2) preferential sensing, i.e., higher importance is given to a part of the covariance matrix. Through experiments, we show that the sensing matrix designed via density evolution can match the state-of-the-art for covariance recovery in the regular sensing paradigm and attain improved performance in the preferential sensing regime. Additionally, we study the feasibility of causal graph structure recovery using the estimated covariance matrix obtained from the compressed measurements.
