Use of Prior Knowledge to Discover Causal Additive Models with Unobserved Variables and its Application to Time Series Data

Abstract: This paper proposes two methods for causal additive models with unobserved variables (CAM-UV). CAM-UV assumes that the causal functions take the form of generalized additive models and that latent confounders are present. First, we propose a method that leverages prior knowledge for efficient causal discovery. Then, we propose an extension of this method for inferring causality in time series data. The original CAM-UV algorithm differs from other existing causal function models in that it does not seek the causal order between observed variables, but rather aims to identify the causes for each observed variable. Therefore, the first proposed method in this paper utilizes prior knowledge, such as understanding that certain variables cannot be causes of specific others. Moreover, by incorporating the prior knowledge that causes precedes their effects in time, we extend the first algorithm to the second method for causal discovery in time series data. We validate the first proposed method by using simulated data to demonstrate that the accuracy of causal discovery increases as more prior knowledge is accumulated. Additionally, we test the second proposed method by comparing it with existing time series causal discovery methods, using both simulated data and real-world data.

• The paper presents the CAM-UV-PK method, which incorporates explicit prior knowledge to rule out impossible causal links, enhancing precision and F-measure.
• It introduces TS-CAM-UV for time series data, using temporal priority to accurately model cause-effect relationships in dynamic settings.
• Both methods are validated on simulated and real-world datasets, demonstrating robust performance compared to existing causal discovery techniques.

Overview

A paper focusing on causal discovery has introduced two significant advancements targeting a specialized subset of causal inference problems. These problems involve situations with unobserved variables—factors that can influence the outcome but are not measured or included in the data. Traditional models often struggle with these hidden confounders, leading to incorrect causal relationships. To tackle this, the authors propose enhancements to the Causal Additive Models with Unobserved Variables (CAM-UV) framework.

Advancements in Causal Discovery

CAM-UV with Prior Knowledge (CAM-UV-PK)

Understanding causal relations when some variables remain unobserved is challenging. The CAM-UV-PK method builds on the existing CAM-UV algorithm. It integrates prior knowledge in the form of explicit statements ruling out certain causes, leading to more accurate causal analysis. The provided prior knowledge helps to define which variables cannot be a cause for others, enhancing causality detection accuracy.

Time Series CAM-UV (TS-CAM-UV)

The second method, TS-CAM-UV, focuses on time series data while incorporating the assumption that past events influence future events but not vice versa. This concept, known as "time priority," is used as prior knowledge to refine causal inferences. The novelty here is that this approach combines the power of functional causal models with the flexibility to include unobserved variables, which is a first in this field.

Validation through Simulated and Real-World Data

The validation of the proposed methods involved rigorous testing against both simulated and real-world datasets. For CAM-UV-PK, the improvement was clear: precision and the overall F-measure increased with the incorporation of more prior knowledge. This proved the usefulness of prior knowledge in refining causal inferences.

Moving to the dynamic field, TS-CAM-UV was compared with existing time series causal discovery methods, explicitly LPCMCI and VarLiNGAM. The results were promising, showing superior or comparable performance across precision, recall, and F-measure, especially as sample sizes increased.

Significance and Future Directions

The significance of these proposed methods lies in their ability to identify causal relationships in the presence of latent confounders accurately. This enhances our understanding of complex systems where not all influencing factors are observable.

While the current focus is on models with acyclical causal graphs, the researchers plan to extend their framework to cyclical models. As data slices become finer, the opportunity for capturing rapid causal effects increases, necessitating methods that can handle contemporaneous effects with cycles.

Conclusion

In conclusion, this paper bridges a critical gap in causal discovery for data with unobserved variables. Whether dealing with static snapshots or evolving over time, CAM-UV-PK and TS-CAM-UV provide robust tools for unraveling the intricate webs of causality that underpin the data-rich world around us.