Layered Synthesis of Latent Gaussian Trees
Layered Synthesis of Latent Gaussian Trees
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潜在高斯树的分层合成
DOI：
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发表时间：
2016
期刊：
影响因子：
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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
提出了一种新的连续编码方案，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。我们证明了这样的编码方案的准确性消失的总变化之间的距离的合成和所需的统计。编码算法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期望的密度，具有紧凑的建模复杂度。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。由于推导出的潜在高斯树的合成可达到的速率区域，我们还量化了由于不可恢复的符号信息的信息损失量。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 successive encoding scheme is proposed to effectively generate a random vector with prescribed joint density that induces a latent Gaussian tree structure. We prove the accuracy of such encoding scheme in terms of vanishing total variation distance between the synthesized and desired statistics. The encoding algorithm relies on the learned structure of tree to use minimal number of common random variables to synthesize the desired density, with compact modeling complexity. 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. Given the derived achievable rate region for synthesis of latent Gaussian trees, we also 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.