Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences

TL;DR

This work introduces a Temporal Latent Variable Structural Causal Model to enable causal discovery under external interference by decomposing the observed causal matrix into adjacency and strength components via a Hadamard product. The model includes latent factors to capture unobserved disturbances and is estimated with variational inference, incorporating expert knowledge through priors. Empirical results across synthetic, fMRI-like, and financial time series show improved precision and F1 scores, with reduced false positives due to latent interferences, and state the method's robustness and practical usefulness. The approach advances causal discovery in realistic settings where hidden factors influence both causal strength and adjacency, and points toward non-linear extensions in future work.

Abstract

Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on observed variables. Since these external factors are often unknown, we introduce latent variables to represent these unobserved factors that affect the observed data. Specifically, to capture the causal strength and adjacency information, we propose a new temporal latent variable structural causal model, incorporating causal strength and adjacency coefficients that represent the causal relationships between variables. Considering that expert knowledge can provide information about unknown interferences in certain scenarios, we develop a method that facilitates the incorporation of prior knowledge into parameter learning based on Variational Inference, to guide the model estimation. Experimental results demonstrate the stability and accuracy of our proposed method.

Figures (5)

• Figure 1: $X_1$ and $X_2$ denote the fMRI data from brain region 1 and brain region 2. $Z$ denotes the unknown external interference, which can be regarded as a latent variable. Due to the existence of a latent variable, the result of classic methods contains spurious correlations.
• Figure 2: Results of different distributions with different average in-degrees of each node.
• Figure 3: Results of different distributions with different numbers of observed variables.
• Figure 4: Results of different distributions with different sample sizes.
• Figure 5: Results of different distributions with different ratios of latent variables.