Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO
Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO
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DOI：
10.1109/tit.2023.3296336
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发表时间：
2023-11-01
影响因子：
2.5
通讯作者：
Babadi，Behtash
中科院分区：
文献类型：
--
作者：
Das，Proloy;Babadi，Behtash
格兰杰因果关系是广泛使用的数据驱动方法之一，用于时间序列数据的因果分析，在包括经济学、分子生物学和神经科学在内的各个领域都有应用。该方法的两个主要挑战是：1）由于有限的数据持续时间而导致的过拟合，以及2）作为混杂因素的相关过程噪声，这两者都导致识别因果影响的错误。通过LASSO的稀疏估计已经成功地解决了参数估计的这些挑战。然而，经典的统计检验格兰杰因果关系诉诸渐近分析的普通最小二乘，这需要长的数据持续时间是有用的，不能免疫的混杂效应。在这项工作中，我们通过引入基于LASSO的统计量并在真实模型允许稀疏自回归表示的假设下研究其非渐近性质来解决这种断开。我们建立了可靠的识别格兰杰因果关系的影响，使用拟议的LASSO为基础的统计基本限制。我们进一步描述了一个简单的阈值规则识别格兰杰因果效应的假阳性错误概率和测试功率，并提供了两种方法来设置阈值的数据驱动的方式。我们目前的模拟研究和应用程序的真实的数据，我们提出的方法来比较普通的最小二乘法和现有的LASSO为基础的方法在检测格兰杰因果关系的影响，这证实了我们的理论结果的性能。
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.