Identifying Structural Biases from Causal Mechanism Shifts

Problem Statement
Causal discovery methods traditionally rely on two strong assumptions: causal sufficiency (all relevant variables are measured) and independent and identically distributed (i.i.d.) data. In practice, these assumptions are frequently violated due to unmeasured confounders and selection bias, leading to spurious dependencies and inaccurate causal inference. While existing methods can sometimes detect latent confounding or selection under specific conditions, distinguishing between them—particularly when data is non-i.i.d. and collected from multiple environments—remains a significant challenge. This paper addresses the problem of identifying structural biases (hidden confounding and selection bias) from causal mechanism shifts observed across different contexts.

Methodology
The authors propose a theoretical framework and a practical algorithm, STRUBI (Structural Bias Identification), to detect and classify structural biases by analyzing how causal mechanisms shift across environments.

1. Theoretical Foundation:

   • The paper distinguishes between intrinsic mechanism shifts (changes in the true data-generating process of a variable) and observed mechanism shifts (changes in the conditional distribution of observed variables).
   • Key Insight: Structural biases induce dependent mechanism shifts, whereas unbiased systems exhibit independent shifts.
     • Hidden Confounding: An intrinsic shift in a latent confounder $Z$ causes observed shifts in its children ($X, Y$) but does not necessarily affect their ancestors or other unrelated variables.
     • Selection Bias: An intrinsic shift in a latent selection variable (collider) $S$ causes observed shifts in all its ancestors ($X, Y, W$).
   • Ancestral Coverage: The authors define "ancestral coverage" ($cov(A)$) as the ratio of a set of variables $A$ to its set of ancestors. They prove that under sparse mechanism shifts, sets of variables affected by selection bias will have an ancestral coverage of 1 (ancestrally closed), whereas sets affected by confounding will typically have a coverage significantly less than 1.

2. The STRUBI Algorithm:

   • Input: Observed data across multiple contexts, an observed causal graph $G$, and thresholds.
   • Step 1 (Shift Detection): For each observed variable, the algorithm performs conditional independence tests (using the KCI test) between contexts to detect if the local mechanism $P(X_i | pa(X_i))$ has changed. This partitions the contexts into blocks of mechanism invariance.
   • Step 2 (Dependency Identification): The algorithm computes the Adjusted Mutual Information (AMI) between the partition patterns of different variables. Variables with high AMI are grouped into connected components, indicating they share a latent cause (either a confounder or a selection variable).
   • Step 3 (Classification): For each identified subset of variables, the algorithm calculates the ancestral coverage on the provided causal graph.
     • If coverage $\ge$ threshold $\tau_2$, the subset is classified as subject to Selection Bias.
     • If coverage $<$ threshold $\tau_2$, the subset is classified as subject to Hidden Confounding.
     • Subsets with low AMI are classified as Unbiased.

Key Contributions

• Identification of Structural Biases: The paper provides a formal proof that structural biases can be identified from non-i.i.d. data by observing dependent mechanism shifts, specifically leveraging the topological difference between confounding (affecting children) and selection (affecting ancestors).
• Non-Parametric Approach: Unlike prior work that often requires parametric assumptions (e.g., linear Gaussian models) or specific data structures (e.g., sequential data), STRUBI is non-parametric and applicable to general causal mechanisms.
• The STRUBI Algorithm: A practical, empirically testable method that integrates mechanism shift detection, mutual information analysis, and graph topology to classify biases and recover affected variable sets.
• Robustness to Graph Error: The method demonstrates robustness even when the input causal graph is inferred rather than known, performing comparably to using the ground truth graph.

Experimental Results
The authors evaluate STRUBI on both synthetic and real-world datasets:

• Synthetic Data: Experiments on Erdős-Rényi graphs with varying sizes show that STRUBI significantly outperforms state-of-the-art baselines (including FCI variants, CoCo, and Latent-Selection methods) in three tasks: detecting the presence of latent variables, recovering the set of affected variables, and classifying the type of bias (confounding vs. selection). STRUBI achieves high F1 scores even when the causal graph is learned (using TOPIC) rather than provided as ground truth.
• Real-World Data (Cell Signaling): A case study on the Sachs et al. flow cytometry dataset demonstrates STRUBI's applicability to complex biological systems. When PKC was withheld to simulate confounding or selection bias, STRUBI correctly identified the bias type and recovered the majority of affected nodes (ancestors in the selection case, children in the confounding case), outperforming competitors like CoCo and JCI-FCI, which failed to accurately recover the affected subsets in the selection bias scenario.

Significance and Claims
The paper claims that STRUBI offers a significant advancement in causal discovery by relaxing the strict i.i.d. and causal sufficiency assumptions. By leveraging the distinct topological signatures of dependent mechanism shifts, the method can distinguish between hidden confounding and selection bias without requiring parametric models. The authors emphasize that their approach works well in practice, accurately recovering affected variable sets and bias types, and outperforming existing methods by a wide margin. They acknowledge limitations, noting that the method assumes the Markov condition and faithfulness, and requires sufficient sample sizes per context and a sufficient number of contexts to reliably detect shifts. However, the results suggest that STRUBI is a robust tool for identifying structural biases in real-world, non-i.i.d. settings.