稀疏Cholesky协方差参数化恢复有序数据潜在结构
Sparse Cholesky covariance parametrization for recovering latent structure in ordered data
摘要：
逆协方差阵的稀疏Cholesky参数化可以被解释为高斯贝叶斯网络;然而，它的对应物，协方差Cholesky因子，迄今为止几乎没有受到关注，尽管有一个自然的解释为有序信号数据的隐藏变量模型。为了填补这一空白，在本文中，我们专注于任意零模式的协方差阵的Cholesky因子。我们讨论如何这些模型也可以扩展，在类比高斯贝叶斯网络，数据没有明显的顺序。对于有序的情况下，我们提出了一种新的估计方法，是基于矩阵损失惩罚，而不是现有的基于回归的方法。这种稀疏模型的Cholesky因子的性能，连同我们的新的估计，在模拟环境中进行评估，以及在空间和时间的真实数据，其中自然的排序之间的变量。我们给出的指导方针，根据实证结果，分析的方法是更适合于每一个设置。
英文摘要：
The sparse Cholesky parametrization of the inverse covariance matrix can be interpreted as a Gaussian Bayesian network; however its counterpart, the covariance Cholesky factor, has received, with few notable exceptions, little attention so far, despite having a natural interpretation as a hidden variable model for ordered signal data. To fill this gap, in this paper we focus on arbitrary zero patterns in the Cholesky factor of a covariance matrix. We discuss how these models can also be extended, in analogy with Gaussian Bayesian networks, to data where no apparent order is available. For the ordered scenario, we propose a novel estimation method that is based on matrix loss penalization, as opposed to the existing regression-based approaches. The performance of this sparse model for the Cholesky factor, together with our novel estimator, is assessed in a simulation setting, as well as over spatial and temporal real data where a natural ordering arises among the variables. We give guidelines, based on the empirical results, about which of the methods analysed is more appropriate for each setting.
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