Inferring deterministic causal relations (1203.3475v1)

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.

• The paper presents a novel IGCI method to infer causal directions in noise-free environments using algorithmic independence between the cause and its mapping function.
• It leverages information geometry and relative entropy measures, employing exponential families to quantify the independence between the distribution of the cause and the deterministic function.
• Empirical results on real-world datasets demonstrate competitive accuracy and linear time complexity, challenging the limits of traditional noise-based causal inference methods.

Deterministic Causal Relations: A Methodological Exploration

The paper "Inferring deterministic causal relations" by Daniušis et al. explores a novel approach to causal inference between two variables connected by an invertible function, even in the absence of noise. Traditional methods, such as the analysis of conditional independencies in causal directed acyclic graphs, grapple with distinguishing causation in Markov-equivalent structures. The authors propose a unique solution to this challenge, focusing on deterministic settings where the task involves distinguishing between $X \rightarrow Y$ and $Y \rightarrow X$.

Methodological Framework

Central to this paper is the concept of algorithmic independence between the distribution of a cause and the function mapping it to the effect. When $X$ causes $Y$, $X$ and the function $f$ are theoretically independent mechanisms. The authors posit that the shortest description of their joint distribution $P(X, Y)$ entails separate descriptions of $P(X)$ and $f$. This idea is anchored in information geometry, employing relative entropy distances to evaluate independence.

Two major formulations arise from this theoretical stance: Postulate 1, which precludes the direct correlation between the distribution of $X$ and the function $f$; and Postulate 2, which extends this notion into the field of relative entropy distances, employing exponential families as reference measures for probability densities.

Empirical Findings

The authors demonstrate the practicality of their approach through empirical studies involving real-world datasets. The proposed Information Geometric Causal Inference (IGCI) method is tested on simulated data scenarios as well as the CauseEffectPairs dataset and German Rhine water level measurements. Remarkably, the method shows competitive accuracy—outperforming conventional noise-dependent models—while retaining computational efficiency due to its linear time complexity in relation to data size.

Theoretical and Practical Implications

Theoretically, the paper opens up a new pathway for causal inference in noise-free environments, providing a framework to exploit deterministic relationships. It challenges existing paradigms by demonstrating that independent mechanisms can be inferred even without the noise structures traditionally deemed necessary for causal identification. Practically, it offers a fast and effective computational tool for real-world causal analysis, broadening the applicability of causal inference techniques to settings previously limited by noise assumptions.

Future Directions

The findings suggest potential avenues for further exploration, especially in understanding the behavior of the method in high-noise scenarios, where its efficacy may diminish. Future research could address confidence estimation in causal direction inference, further enhancing the robustness and utility of the technique.

In conclusion, the paper provides a detailed methodological analysis and empirical justification for deterministic causal inference, contributing significantly to the broader field of causal discovery. While the method shows promise in both its theoretical foundation and empirical validation, ongoing research is vital to harness its full potential in diverse application domains.