高斯树的树结构综合
Tree Structured Synthesis of Gaussian Trees
摘要：
提出了一种新的合成方案，以有效地产生一个随机向量与指定的联合密度，诱导（潜在的）高斯树结构。合成的质量通过合成的统计量和期望的统计量之间的总变化距离来衡量。所提出的分层连续编码方案依赖于学习的树结构，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。
英文摘要：
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the synthesized and desired statistics. The proposed layered and successive encoding scheme relies on the learned structure of tree to use minimal 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 simulate 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
