隐高斯树的分层综合
Layered Synthesis of Latent Gaussian Trees
摘要：
提出了一种新的合成方案，以产生一个具有指定的联合密度，诱导（潜在）高斯树结构的随机向量。合成的质量通过使合成的统计量和期望的统计量之间的总变化距离消失来显示。所提出的分层和连续的合成方案依赖于学习的树的结构，使用足够数量的公共随机变量来合成所需的密度。我们描述了多层潜在高斯树的速率元组的可达速率区域，通过该区域确定了合成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在树的顶层的潜变量，加性独立高斯噪声，和伯努利符号输入，捕捉变量之间的相关性符号的模糊性。我们已经表明，这种模糊性可以进一步帮助降低基础高斯树的合成速率。
英文摘要：
A new synthesis scheme is proposed to generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is shown by vanishing total variation distance between the synthesized and desired statistics. The proposed layered and successive synthesis scheme relies on the learned structure of tree to use sufficient number of common random variables to synthesize the desired density. We characterize the achievable rate region for the rate tuples of multi-layer latent Gaussian tree, through which the number of bits needed to synthesize such Gaussian joint density are determined. The random sources used in our algorithm are the latent variables at the top layer of tree, the additive independent Gaussian noises, and the Bernoulli sign inputs that capture the ambiguity of correlation signs between the variables. We have shown that such ambiguity can further help in reducing the synthesis rates for the underlying Gaussian trees.
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