Clustering and Structural Robustness in Causal Diagrams
Authors: Santtu Tikka, Jouni Helske, Juha Karvanen; 24(195):1−32, 2023.
Abstract
Causal relations are commonly represented and visualized using graphs. While this approach is concise and clear for a small number of variables, it becomes impractical and less clear as the number of variables increases. Clustering variables is a natural way to reduce the size of the causal diagram, but it must be done carefully to avoid altering the essential properties of the causal relations. In this study, we introduce a specific type of cluster, called a transit cluster, which guarantees the preservation of the identifiability properties of causal effects under certain conditions. We present a comprehensive algorithm for identifying all transit clusters in a given graph and demonstrate how clustering can simplify the identification of causal effects. Additionally, we investigate the inverse problem, where a clustered graph is given, and explore extended graphs that maintain the identifiability properties of causal effects. We establish a close relationship between this structural robustness and transit clusters.
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