The Convex Mixture Distribution: Granger Causality for Categorical Time Series
The Convex Mixture Distribution: Granger Causality for Categorical Time Series
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DOI：
10.1137/20m133097x
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发表时间：
2021-01-01
影响因子：
3.6
通讯作者：
Shojaie，Ali
中科院分区：
文献类型：
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作者：
Tank，Alex;Li，Xiudi;Shojaie，Ali
我们提出了一个基于混合转移分布（MTD）模型的多元分类时间序列的格兰杰因果网络学习框架。传统上，MTD 受到非凸目标、不可辨识性和局部最优的困扰。为了规避这些问题，我们将 MTD 中的推理重新定义为凸问题。新的公式促进了 MTD 在高维多元时间序列中的应用。作为基线，我们还制定了多项逻辑转移分布（mLTD）模型。虽然它是自回归伯努利广义线性模型的直接扩展，但之前尚未应用于多元分类时间序列的分析。我们建立了 MTD 模型的可识别性条件，并将其与 mLTD 的可识别性条件进行比较。我们基于我们提出的凸公式进一步设计了新颖且有效的 MTD 优化算法，并在模拟和真实数据实验中比较了 MTD 和 mLTD。最后，我们建立了高维凸 MTD 的一致性。我们的方法同时提供了分类时间序列中网络推理方法的比较，并为使用 MTD 模型进行现代、正则化推理打开了大门。
We present a framework for learning Granger causality networks for multivariate categorical time series based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective, nonidentifiability, and the presence of local optima. To circumvent these problems, we recast inference in the MTD as a convex problem. The new formulation facilitates the application of MTD to high-dimensional multivariate time series. As a baseline, we also formulate a multinomial logistic transition distribution (mLTD) model. While it is a straightforward extension of autoregressive Bernoulli generalized linear models, it has not been previously applied to the analysis of multivariate categorical time series. We establish identifiability conditions of the MTD model and compare them to those for mLTD. We further devise novel and efficient optimization algorithms for MTD based on our proposed convex formulation and compare the MTD and mLTD in both simulated and real data experiments. Finally, we establish consistency of the convex MTD in high dimensions. Our approach simultaneously provides a comparison of methods for network inference in categorical time series and opens the door to modern, regularized inference with the MTD model.