Synthesis of Gaussian trees with correlation sign ambiguity: An information theoretic approach
Synthesis of Gaussian trees with correlation sign ambiguity: An information theoretic approach
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具有相关符号模糊性的高斯树的综合：一种信息论方法
DOI：
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发表时间：
2016
期刊：
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通讯作者：
Jing Deng
中科院分区：
文献类型：
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作者：
A. Moharrer;Shuangqing Wei;G. Amariucai;Jing Deng
提出了一种新的分层编码方案，有效地产生一个具有指定的联合密度，诱导潜在的高斯树结构的随机向量。编码算法依赖于学习的树的结构，使用最少数量的公共随机变量来合成所需的密度，我们认为这样的算法也是计算效率高的。我们描述了多层潜在高斯树的速率元组的可达速率区域，通过该区域确定了模拟这种高斯联合密度所需的比特数。在我们的算法中使用的随机源是潜在的变量在树的顶层沿着与伯努利符号输入，捕捉变量之间的相关性的迹象。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。作为一个副产品，确定可实现的速率区域，我们量化的信息损失量由于不可恢复的标志信息。它示出，最大限度地提高可实现的速率区域相当于找到最坏情况下的伯努利符号输入的最大量的符号信息丢失的密度。
A new layered encoding scheme is proposed to effectively generate a random vector with prescribed joint density that induces a latent Gaussian tree structure. The encoding algorithm relies on the learned structure of tree to use minimal number of common random variables to synthesize the desired density, which we argue such algorithm is also computationally efficient. We characterize the achievable rate region for the rate tuples of multi-layer latent Gaussian tree, through which the number of bits needed to simulate such Gaussian joint density are determined. The random sources used in our algorithm are the latent variables at the top layer of tree along with Bernoulli sign inputs, which capture the correlation signs between the variables. 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. As a by-product of determining the achievable rate region, we quantify the amount of information loss due to unrecoverable sign information. It is shown that maximizing the achievable rate-region is equivalent to finding the worst case density for Bernoulli sign inputs where maximum amount of sign information is lost.