[Paper Review] Inferring deterministic causal relations

Povilas Daniušis, Dominik Janzing+5 more|arXiv (Cornell University)|Mar 15, 2012

Bayesian Modeling and Causal Inference8 references110 citations

TL;DR

This paper proposes a method to infer causal direction between two variables linked by a deterministic, invertible function, even without observational noise. By exploiting asymmetries in the interplay between the functional form and the marginal distribution of the cause—rooted in information geometry—it demonstrates that the effect distribution encodes information about the function, enabling causal discovery in noise-free settings with strong empirical validation across diverse datasets.

ABSTRACT

We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.

Motivation & Objective

• To address the challenge of causal inference in deterministic systems where traditional noise-based methods fail.
• To identify structural asymmetries between cause and effect in deterministic functional relationships.
• To develop a method that leverages the independence of the functional form and the cause's distribution to infer causal direction.
• To extend causal discovery techniques beyond the noisy regime into the deterministic and low-noise cases.
• To validate the method empirically on real-world datasets from diverse domains.

Proposed method

• The method assumes that the functional form and the marginal distribution of the cause are statistically independent.
• It exploits the fact that the resulting distribution of the effect depends on the functional form, creating an asymmetry detectable via information geometry.
• The approach uses the Fisher information metric to quantify the geometric relationship between the function and the distribution, identifying which variable is more likely to be the cause.
• It formulates a criterion based on the complexity of the effect distribution, favoring the direction where the function and distribution are less dependent.
• The method is theoretically justified in the low-noise limit, showing robustness to small perturbations.
• Empirical validation is performed using real-world datasets across multiple domains to assess performance.

Experimental results

Research questions

• RQ1 Can causal direction be inferred in deterministic systems where no additive noise is present?
• RQ2 What structural asymmetries exist between cause and effect in deterministic functional relationships?
• RQ3 How can the independence of the functional form and the cause's distribution be leveraged for causal discovery?
• RQ4 Does the proposed method remain valid in the low-noise regime approaching determinism?
• RQ5 Can the method generalize across diverse real-world datasets with varying functional forms?

Key findings

• The method successfully infers causal direction in deterministic and low-noise settings by detecting asymmetries in the function-distribution interaction.
• Theoretical analysis confirms the method's validity in the low-noise limit, showing continuity with noisy causal inference frameworks.
• Empirical results demonstrate strong performance across multiple real-world datasets, confirming the method's practical utility.
• The approach is grounded in information geometry, providing a principled link between functional form and distributional properties.
• The method outperforms baseline approaches in deterministic settings where noise-based methods fail.
• The study establishes that even in the absence of noise, identifiable asymmetries exist that can be exploited for causal discovery.