基于信息论的相关符号模糊高斯树的合成
Synthesis of Gaussian Trees with Correlation Sign Ambiguity: An Information Theoretic Approach
摘要：
在潜在高斯树中，变量之间的成对相关符号本质上是不可恢复的。这种信息是至关重要的，因为它完全决定了两个变量相关联的方向。在这项工作中，我们诉诸信息理论的方法来实现两个基本目标：首先，我们量化的信息损失量由于不可恢复的迹象信息。第二，我们展示了这些信息在确定最大可达速率区域中的重要性，在该区域中，可以合成所观察到的输出向量，给出其概率密度函数。特别是，我们建模的图形模型作为一个通信信道，并提出了一个新的分层编码框架，合成观察到的数据，使用上层高斯输入和独立的伯努利相关符号输入从每一层。我们找到了多层潜在高斯消息的速率元组的可实现速率区域，以合成所需的观测量。
英文摘要：
In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: First, we quantify the amount of information loss due to unrecoverable sign information. Second, we show the importance of such information in determining the maximum achievable rate region, in which the observed output vector can be synthesized, given its probability density function. In particular, we model the graphical model as a communication channel and propose a new layered encoding framework to synthesize observed data using upper layer Gaussian inputs and independent Bernoulli correlation sign inputs from each layer. We find the achievable rate region for the rate tuples of multi-layer latent Gaussian messages to synthesize the desired observables.
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