The Autoregressive Linear Mixture Model: A Time-Series Model for an Instantaneous Mixture of Network Processes
The Autoregressive Linear Mixture Model: A Time-Series Model for an Instantaneous Mixture of Network Processes
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DOI：
10.1109/tsp.2020.3012946
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发表时间：
2020-07
影响因子：
5.4
通讯作者：
Addison W. Bohannon;Vernon J. Lawhern;Nicholas R. Waytowich;R. Balan
中科院分区：
文献类型：
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作者：
Addison W. Bohannon;Vernon J. Lawhern;Nicholas R. Waytowich;R. Balan
向量自回归模型为多变量时间序列数据提供了一个简单的生成模型。向量自回归模型的自回归系数描述了一个网络过程。然而，在宏观经济学或神经成像等现实应用中，时间序列数据不是来自孤立的网络过程，而是来自多个网络过程的同时发生。标准的向量自回归模型无法提供有关此类时间序列数据的基本结构的见解。在这项工作中，我们提出了自回归线性混合（ALM）模型。ALM提出将时间序列数据分解为我们称之为自回归分量的共现网络过程。我们还提出了一个非凸的似然估计拟合的ALM模型，并表明它可以使用近端交替线性化最小化（PALM）算法来解决。我们在合成和真实世界的脑电图数据上验证了ALM，表明我们可以消除与不同网络过程相对应的任务相关自回归分量的歧义。
Vector autoregressive models provide a simple generative model for multivariate, time-series data. The autoregressive coefficients of the vector autoregressive model describe a network process. However, in real-world applications such as macroeconomics or neuroimaging, time-series data arise not from isolated network processes but instead from the simultaneous occurrence of multiple network processes. Standard vector autoregressive models cannot provide insights about the underlying structure of such time-series data. In this work, we present the autoregressive linear mixture (ALM) model. The ALM proposes a decomposition of time-series data into co-occurring network processes that we call autoregressive components. We also present a non-convex likelihood-based estimator for fitting the ALM model and show that it can be solved using the proximal alternating linearized minimization (PALM) algorithm. We validate the ALM on both synthetic and real-world electroencephalography data, showing that we can disambiguate task-relevant autoregressive components that correspond with distinct network processes.