Causal discovery on vector-valued variables and consistency-guided aggregation
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向量值变量的因果发现与一致性引导的聚合
- 研究问题
- 当观测变量本身是高维向量时，如何开展因果图发现，并判断降维聚合是否保留该任务所需的独立性信息？
- 方法与思路
- 作者采用约束型因果发现方法，基于独立性模型兼容性及部分聚合构造三种一致性评分，并提出优化评分的 Adag 包装算法。
- 材料陈述的贡献
- 摘要提出区分因果抽象的一致性与具体发现任务中的聚合一致性，并以合成非时序及空间时间数据开展实验评估。
- 阅读关注点
- 应核对三种评分各自衡量什么、聚合前后独立性关系如何比较，以及评分优化与因果图可靠性之间的理论联系。
- 阅读边界
- 这是预印本，同行评审及期刊接收未获核实；摘要未说明具体模型假设，也不能据此认定聚合保留全部因果信息。
原文摘要
Causal discovery (CD) aims to discover the causal graph underlying the data generation mechanism of observed variables. In many real-world applications, the observed variables are vector-valued, such as in climate science where variables are defined over a spatial grid and the task is called spatio-temporal causal discovery. We motivate CD in vector-valued variable setting while considering different possibilities for the underlying model, and highlight the pitfalls of commonly-used approaches when compared to a fully vectorized approach. Furthermore, often the vector-valued variables are high-dimensional, and aggregations of the variables, such as averages, are considered in interest of efficiency and robustness. In the absence of interventional data, testing for the soundness of aggregate variables as consistent abstractions that map a low-level to a high-level structural causal model (SCM) is hard, and recent works have illustrated the stringency of conditions required for testing consistency. In this work, we take a careful look at the task of vector-valued CD via constraint-based methods, focusing on the problem of consistency of aggregation for this task. We derive three aggregation consistency scores, based on compatibility of independence models and (partial) aggregation, that quantify different aspects of the soundness of an aggregation map for the CD problem. We present the argument that the consistency of causal abstractions must be separated from the task-dependent consistency of aggregation maps. As an actionable conclusion of our findings, we propose a wrapper Adag to optimize a chosen aggregation consistency score for aggregate-CD, to make the output of CD over aggregate variables more reliable. We supplement all our findings with experimental evaluations on synthetic non-time series and spatio-temporal data.