Federated Causal Discovery Across Heterogeneous Datasets under Latent Confounding

TL;DR

fedCI is introduced, a federated conditional independence test that rigorously handles heterogeneous datasets with non-identical sets of variables, site-specific effects, and mixed variable types, including continuous, ordinal, binary, and categorical variables, and fedCI-IOD, a federated extension of the Integration of Overlapping Datasets algorithm that replaces its meta-analysis strategy and enables federated causal discovery under latent confounding across distributed and heterogeneous datasets.

Abstract

Causal discovery across multiple datasets is often constrained by data privacy regulations and cross-site heterogeneity, limiting the use of conventional methods that require a single, centralized dataset. To address these challenges, we introduce fedCI, a federated conditional independence test that rigorously handles heterogeneous datasets with non-identical sets of variables, site-specific effects, and mixed variable types, including continuous, ordinal, binary, and categorical variables. At its core, fedCI uses a federated Iteratively Reweighted Least Squares (IRLS) procedure to estimate the parameters of generalized linear models underlying likelihood-ratio tests for conditional independence. Building on this, we develop fedCI-IOD, a federated extension of the Integration of Overlapping Datasets (IOD) algorithm, that replaces its meta-analysis strategy and enables, for the fist time, federated causal discovery under latent confounding across distributed and heterogeneous datasets. By aggregating evidence federatively, fedCI-IOD not only preserves privacy but also substantially enhances statistical power, achieving performance comparable to fully pooled analyses and mitigating artifacts from low local sample sizes. Our tools are publicly available as the fedCI Python package, a privacy-preserving R implementation of IOD, and a web application for the fedCI-IOD pipeline, providing versatile, user-friendly solutions for federated conditional independence testing and causal discovery.

Figures (12)

• Figure 1: Comparison of constraint-based causal discovery results of the IOD algorithm in its original form using meta-analysis Tillman2011 and our proposed federated adaptation. Differences in the CI tests led to different local graphs for each client. Merging these local results into one PAG that adheres to all constraints was impossible for meta-analysis, but our federated approach was able to find the correct data-generating PAG.
• Figure 2: Schematic overview of federated causal discovery, including clients with non-identical variable sets and a managing server which are in potentially seperate networks, obtaining individual as well as unified PAGs. In Appendix \ref{['sec:webapp appx']}, screenshots of our web application showcase each step of this process.
• Figure 3: Illustration of the federated CI test procedure for $X \perp\!\!\!\perp Y \mid Z$. Clients $C_1$ and $C_2$ hold data on variables $\{X, Y, Z\}$, while client $C_3$ only observes $\{Y, Z\}$. Since the test requires data on $X$, client $C_3$ cannot contribute, it sends masked null-contributions. The server coordinates the federated IRLS fitting procedure to obtain the global models $M_0^X$, $M_1^X$, $M_0^Y$, and $M_1^Y$ and then aggregates the local log-likelihoods for each model from the contributing clients to compute test statistics ($T^X, T^Y$), $p$-values ($p^X, p^Y$), and a final combined $p$-value ($p$).
• Figure 4: Accuracy of CI tests across (a) $4$, (b) $8$, and (c) $12$ partitions. The $y$-axis represents the agreement between test decisions and the true distributional dependence and independence, while the $x$-axis denotes the total sample size. Results for fedCI (solid line) nearly perfectly align with the pooled baseline (dotted line), whereas Fisher's method (dashed line) exhibits performance degradation as the number of partitions increases.
• Figure 5: Boxplot of log-ratios of $p$-values for fedCI and Fisher's method relative to the pooled baseline on $1,000$ samples, across different numbers of partitions (sites). FedCI remains centered at zero with low variance, while Fisher's method increasingly deviates with a positive bias as partitions grows.