I-CAM-UV: Integrating Causal Graphs over Non-Identical Variable Sets Using Causal Additive Models with Unobserved Variables

TL;DR

This work proposes an approach named I-CAM-UV to integrate CAM-UV results by enumerating all consistent causal graphs and shows that the ground truth causal graph has structural consistency with the information of CAM-UV on each dataset.

Abstract

Causal discovery from observational data is a fundamental tool in various fields of science. While existing approaches are typically designed for a single dataset, we often need to handle multiple datasets with non-identical variable sets in practice. One straightforward approach is to estimate a causal graph from each dataset and construct a single causal graph by overlapping. However, this approach identifies limited causal relationships because unobserved variables in each dataset can be confounders, and some variable pairs may be unobserved in any dataset. To address this issue, we leverage Causal Additive Models with Unobserved Variables (CAM-UV) that provide causal graphs having information related to unobserved variables. We show that the ground truth causal graph has structural consistency with the information of CAM-UV on each dataset. As a result, we propose an approach named I-CAM-UV to integrate CAM-UV results by enumerating all consistent causal graphs. We also provide an efficient combinatorial search algorithm and demonstrate the usefulness of I-CAM-UV against existing methods.

Figures (22)

• Figure 1: Illustration of unobserved causal path (UCP) and unobserved backdoor path (UBP).
• Figure 2: Example of CAM-UV. A UCP $v_4 \rightarrow v_5 \rightarrow v_6$ and a UBP $v_2 \leftarrow v_1 \rightarrow v_3$ are found. The dashed lines indicate undirected edges of the resulting mixed graph.
• Figure 3: Example of inputs on a scenario we consider (left) and their simple overlapping (right).
• Figure 4: Example of I-CAM-UV on the input of Figure \ref{['fig:inputs']}.
• Figure 5: Example of I-CAM-UV resulting a unique DAG.

Theorems & Definitions (15)

• Definition 1: Unobserved Causal Path (UCP)
• Definition 2: Unobserved Backdoor Path (UBP)
• Definition 3
• Theorem 1
• Example 1
• Example 2
• Definition 4
• Example 3
• Example 4
• Definition 5