Causal Inference on Discrete Data Using Additive Noise Models.

Area of Science:

• Causal inference
• Machine learning
• Statistics

Background:

• Inferring causal structure from data is crucial in science.
• Existing methods based on additive noise models primarily apply to continuous variables.
• Causal discovery with discrete variables remains a significant challenge.

Purpose of the Study:

• To extend additive noise models for causal inference to discrete variables.
• To develop an efficient algorithm for causal discovery in discrete settings.
• To validate the proposed method on synthetic and real-world datasets.

Main Methods:

• Extension of additive noise models to discrete and finite-state variables.
• Theoretical proof demonstrating the rarity of fitting additive noise models in both causal directions.
• Development of an efficient algorithm for causal inference on discrete data.

Main Results:

• Additive noise models are shown to be rarely applicable in both directions for discrete variables.
• The proposed algorithm successfully infers causal direction from finite samples of discrete variables.
• Empirical validation confirms the algorithm's effectiveness on both synthetic and real datasets.

Conclusions:

• Additive noise models provide a viable framework for causal inference with discrete variables.
• The developed algorithm offers an efficient solution for causal discovery in discrete domains.
• This work bridges a gap in causal inference methodologies, enabling applications with discrete data.