On Causal Discovery in the Presence of Deterministic Relations

Loka Li, Hanin Al Ghothani, Biwei Huang, Guangyi Chen, Jiji Zhang, Shahar Harel, Kun Zhang

Primary Area: causal reasoning

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Keywords: Causal discovery, score-based method, deterministic relation

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TL;DR: We find that exact score-based methods under mild assumptions can naturally address deterministic challenges, and propose a novel method called DGES.

Abstract:

Many causal discovery methods typically rely on the assumption of independent noise, yet real-life situations often involve deterministic relationships. In these cases, observed variables are represented as deterministic functions of their parental variables, without noise.
When determinism is present, constraint-based methods encounter challenges due to the violation of the faithfulness assumption. In this paper, we excitingly find, supported by both theoretical analysis and empirical evidence, that score-based methods with exact search can naturally address the issues of deterministic relations under rather mild assumptions. Nonetheless, exact score-based methods can be computationally expensive. To enhance the efficiency and scalability, we develop a novel framework for causal discovery that can detect and handle deterministic relations, called Determinism-aware Greedy Equivalent Search (DGES). DGES comprises three phases: (1) run Greedy Equivalent Search (GES) to obtain an initial graph, (2) identify deterministic clusters (i.e., variables with deterministic relationships), and (3) perform exact search exclusively on each deterministic cluster and its neighbors. The proposed DGES accommodates both linear and nonlinear causal relationships, as well as both continuous and discrete data types. Furthermore, we investigate the identifiability conditions of DGES. We conducted extensive experiments on both simulated and real-world datasets to show the efficacy of our proposed method.

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Submission Number: 1517