论文标题
稀疏的cholesky协方差参数化用于在有序数据中恢复潜在结构
Sparse Cholesky covariance parametrization for recovering latent structure in ordered data
论文作者
论文摘要
逆协方差矩阵的稀疏cholesky参数化可以解释为高斯贝叶斯网络。然而，尽管有自然的解释是有序信号数据的隐藏变量模型，但它的同行是协方差cholesky因子，但很少有明显的注意力。为了填补这一空白，在本文中，我们重点介绍协方差矩阵的cholesky因子中的任意零模式。我们讨论了这些模型如何与高斯贝叶斯网络类似于没有明显顺序的数据。对于有序场景，我们提出了一种基于矩阵损失惩罚的新型估计方法，而不是现有的基于回归的方法。在模拟设置中评估了这种稀疏模型的稀疏模型以及我们的新估计器，以及在变量之间出现自然排序的空间和时间真实数据。我们根据经验结果给出了指南，涉及哪种分析的方法更适合每种设置。
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.
