地球科学与遥感观测数据的因果推断
Causal Inference in Geoscience and Remote Sensing from Observational Data
摘要：
从观测数据中建立随机变量之间的因果关系可能是当今\blue{science}中最重要的挑战。在遥感和地球科学中，这对于更好地了解地球系统和各控制过程之间复杂的相互作用具有特别的意义。在本文中，我们专注于观察因果推断，因此，我们试图估计正确的方向因果关系使用一组有限的经验数据。此外，我们专注于更复杂的双变量场景，需要强假设，没有条件独立性测试可以使用。特别是，我们探索（非确定性）加性噪声模型的框架，它依赖于原因和生成机制之间的独立性原则。这种原理的实际算法实例仅需要1）在前向和后向方向上的两个回归模型，以及2）所获得的残差与观测值之间的{ \em统计独立性}的估计。导致更多独立残差的方向被确定为原因。相反，我们提出了一个标准，使用{ \em灵敏度}（衍生物）的依赖估计，灵敏度标准允许识别样本最影响的依赖措施，因此该标准是鲁棒的虚假检测。我们说明了在收集的28个地球科学因果推断问题，在辐射传输模型模拟和机器学习仿真器在植被参数建模涉及182个问题的数据库中的性能，并在评估不同的回归模型在碳循环问题的影响。该标准在所有情况下都达到了最先进的检测率，它通常对噪声源和失真具有鲁棒性。
英文摘要：
Establishing causal relations between random variables from observational data is perhaps the most important challenge in today's \blue{science}. In remote sensing and geosciences this is of special relevance to better understand the Earth's system and the complex interactions between the governing processes. In this paper, we focus on observational causal inference, thus we try to estimate the correct direction of causation using a finite set of empirical data. In addition, we focus on the more complex bivariate scenario that requires strong assumptions and no conditional independence tests can be used. In particular, we explore the framework of (non-deterministic) additive noise models, which relies on the principle of independence between the cause and the generating mechanism. A practical algorithmic instantiation of such principle only requires 1) two regression models in the forward and backward directions, and 2) the estimation of {\em statistical independence} between the obtained residuals and the observations. The direction leading to more independent residuals is decided to be the cause. We instead propose a criterion that uses the {\em sensitivity} (derivative) of the dependence estimator, the sensitivity criterion allows to identify samples most affecting the dependence measure, and hence the criterion is robust to spurious detections. We illustrate performance in a collection of 28 geoscience causal inference problems, in a database of radiative transfer models simulations and machine learning emulators in vegetation parameter modeling involving 182 problems, and in assessing the impact of different regression models in a carbon cycle problem. The criterion achieves state-of-the-art detection rates in all cases, it is generally robust to noise sources and distortions.
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