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arXiv 1702.08575cs.LGstat.ML
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具有潜过程的学习向量自回归模型

Learning Vector Autoregressive Models with Latent Processes

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校协调科学实验室);Department of ISE, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校工业与系统工程系);Department of ECE, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校电气与计算机工程系);Department of Philosophy, Carnegie Mellon University(卡内基梅隆大学哲学系)

Saber Salehkaleybar, Jalal Etesami, Negar Kiyavash, Kun Zhang

摘要:

研究了向量自回归(VAR)模型中,当过程的子集是潜在的时,从样本中学习过程间转移矩阵的支持度问题。众所周知,忽略潜在过程的影响可能会导致对观测过程之间影响的非常不同的估计,我们关心的是识别观测过程之间的影响,潜在过程之间的影响,以及从潜在过程到观测过程的影响。我们证明了在VAR模型上,在一定的条件下,可以成功地确定观测过程之间的转移矩阵的支持度和任意两个观测过程之间的所有潜在路径的长度.从潜在路径的长度,我们重建的潜在子图(代表的潜在过程之间的影响),唯一的最小数量的变量,如果它的拓扑结构是一个有向树。此外,我们提出了一个算法,找到所有可能的最小潜在图的潜在路径的长度在一定的条件下。我们的结果适用于非高斯和高斯的情况下,各种合成和真实世界的数据集上的实验结果验证了我们的理论结果。

英文摘要:

We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the latent processes may lead to very different estimates of the influences among observed processes, and we are concerned with identifying the influences among the observed processes, those between the latent ones, and those from the latent to the observed ones. We show that the support of transition matrix among the observed processes and lengths of all latent paths between any two observed processes can be identified successfully under some conditions on the VAR model. From the lengths of latent paths, we reconstruct the latent subgraph (representing the influences among the latent processes) with a minimum number of variables uniquely if its topology is a directed tree. Furthermore, we propose an algorithm that finds all possible minimal latent graphs under some conditions on the lengths of latent paths. Our results apply to both non-Gaussian and Gaussian cases, and experimental results on various synthetic and real-world datasets validate our theoretical results.

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。

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