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A Survey on Federated Causal Discovery and Inference

This paper presents a comprehensive survey of federated causal discovery and inference, offering a unified framework that categorizes existing methods across multiple dimensions, formalizes their connection as complementary stages of a causal reasoning pipeline, and identifies key challenges and future research directions.

Original authors: Xianjie Guo, Yuwei Wang, Guodu Xiang, Xiaoli Tang, Kui Yu, Han Yu, Qiang Yang

Published 2026-06-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Xianjie Guo, Yuwei Wang, Guodu Xiang, Xiaoli Tang, Kui Yu, Han Yu, Qiang Yang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to solve a massive mystery: Why do things happen?

In the world of data, this is called Causal Reasoning. It has two main jobs:

Causal Discovery: Figuring out the map of who causes what (e.g., Does smoking cause cancer, or is it just that smokers also drink coffee?).
Causal Inference: Measuring exactly how much one thing changes another (e.g., If we stop smoking, how much does the cancer rate drop?).

Usually, to solve these mysteries, you need to gather all the clues (data) into one giant room. But in the real world, data is scattered. Hospitals, banks, and factories hold their own private records. They can't share them because of privacy laws (like HIPAA or GDPR) or because they don't trust each other.

Enter Federated Learning. Think of this as a "Secret Detective Agency." Instead of bringing all the clues to one room, the detectives (computers) stay in their own offices. They only share their conclusions or notes with a central coordinator, never showing their raw files.

This paper is a comprehensive guidebook for a new, super-specialized version of this agency: Federated Causal Discovery and Inference (FCD & FCI). It maps out how to solve these causal mysteries while keeping everyone's data locked in their own safes.

Here is the breakdown of the paper's journey, explained simply:

1. The Two Main Missions

The paper splits the work into two distinct but connected missions:

Mission A: Federated Causal Discovery (FCD) – "Drawing the Map"
- The Goal: To build a complete "Cause-and-Effect Map" (a graph) showing how variables connect.
- The Challenge: How do you draw a map when no single detective has seen all the terrain?
- The Solution: Each detective draws a small local map based on their own clues. They send their map fragments to the central HQ. The HQ stitches them together to form one giant, global map without ever seeing the raw terrain.
- The Paper's Taxonomy: The authors organize all the different ways to do this into three categories:
  - How they think: Do they test rules (Constraint-based), try to find the best score (Score-based), or use smooth math (Continuous Optimization)?
  - How they are arranged: Do they all have the same variables (Horizontal), different variables for the same people (Vertical), or a mix (Hybrid)?
  - What they see: Do they try to map the whole world (Global) or just the neighborhood around one specific variable (Local)?
Mission B: Federated Causal Inference (FCI) – "Measuring the Impact"
- The Goal: Once the map is drawn, how much does a specific action (like a new drug) change the outcome (like patient recovery)?
- The Challenge: If you just combine data from different hospitals, you might get the wrong answer because the hospitals treat different types of patients.
- The Solution: The detectives use special math tricks (like weighting or matching) to compare apples to apples across different locations, all without sharing the patient names.
- The Paper's Taxonomy: They categorize these methods by:
  - What they measure: The average effect on everyone (ATE) or the effect on specific individuals (ITE/CATE).
  - How they calculate it: Using weights, matching people up, deep learning AI, or Bayesian statistics.

2. The Secret Connection: The Pipeline

The paper makes a crucial point: Discovery and Inference are best friends.

You usually need the Map (Discovery) first to know which variables to adjust for when measuring the Impact (Inference).
The authors visualize this as a Pipeline: First, the team builds the map together. Then, they use that map to calculate the treatment effect.
The Catch: If the map is wrong, the measurement will be wrong. The paper highlights that we need to be careful about how errors in the first step mess up the second step, especially when privacy is involved.

3. The Hurdles (Why is this hard?)

The paper points out several "villains" that make this difficult:

The "Different Languages" Problem (Heterogeneity): Hospital A might measure blood pressure in mmHg, while Hospital B uses a different scale. Or, Hospital A might have data on "smoking" but Hospital B doesn't. The algorithms have to speak across these differences.
The "Missing Clues" Problem (Missing Data): Sometimes data is just gone. If Hospital A is missing 50% of its records and Hospital B is missing 10%, combining them is tricky.
The "Privacy vs. Accuracy" Trade-off: To keep data safe, we add "noise" (like static on a radio). Too much noise, and the map is blurry; too little, and privacy is broken. Finding the sweet spot is a major challenge.
The "Communication Cost": Sending a whole map (or a huge AI model) back and forth takes a lot of time and bandwidth. The paper looks for ways to send only the "essential notes" instead of the whole book.

4. Where is this used? (According to the paper)

The authors list specific real-world scenarios where this "Secret Detective Agency" is already being tested or proposed:

Healthcare: Comparing drug effectiveness across different countries without sharing patient records (e.g., COVID-19 vaccine studies, Alzheimer's research).
Manufacturing: Figuring out why a machine in one factory is producing defects by comparing it to other factories without revealing trade secrets.
Social Media: Understanding how content moderation affects user engagement across different platforms without seeing individual user data.
Economics: Evaluating government policies across different regions without centralizing sensitive financial data.
Fairness: Checking if hiring algorithms are biased against certain groups across different companies without revealing the applicants' identities.

5. What's Next? (The Open Challenges)

The paper concludes by saying the field is young and needs more work:

Better Maps: We need better ways to handle "Vertical" setups (where different people have different variables).
Stronger Privacy: We need mathematical guarantees that no one can cheat and steal data from the "notes" being shared.
Standard Tests: We need a common "exam" or benchmark so researchers can fairly compare their methods.
AI Assistants: Could Large Language Models (LLMs) help suggest the causal maps to speed things up?

Summary

In short, this paper is a roadmap for a new era of data science. It teaches us how to solve the "Who caused what?" and "How much did it change?" questions when the data is scattered across the world and locked behind privacy walls. It organizes the messy landscape of current research into a clear structure, showing us where the tools are, where they are missing, and how to build a better, more private future for data-driven decision-making.

Technical Summary: A Survey on Federated Causal Discovery and Inference

1. Problem Definition

The paper addresses the critical challenge of performing causal reasoning when data is distributed across multiple institutions (e.g., hospitals, banks, research centers) that cannot or will not share raw records due to privacy regulations (e.g., GDPR, HIPAA) and communication constraints. While Federated Learning (FL) has successfully enabled collaborative supervised learning, its integration with causal frameworks introduces distinct difficulties.

The paper focuses on two complementary tasks:

Federated Causal Discovery (FCD): The task of recovering the global causal structure (Directed Acyclic Graph, DAG) from distributed observational data without centralizing raw data.
Federated Causal Inference (FCI): The task of quantifying causal effects (e.g., Average Treatment Effect, ATE) across distributed populations, requiring the adjustment for confounders that may vary in distribution or mechanism across sites.

Key challenges identified include:

Structural Constraints: Enforcing global acyclicity in a distributed setting is combinatorially difficult.
Heterogeneity: Clients often possess heterogeneous causal mechanisms (different conditional distributions $P(X_i | Pa(X_i))$ ) and may observe non-identical sets of variables, violating the assumptions of standard FL.
Identifiability: Causal conclusions depend on sufficient conditioning sets and functional assumptions, which become complex when data is partitioned.

2. Methodology and Taxonomy

The paper provides a systematic review organized through multi-dimensional taxonomies, distinguishing it from prior broad surveys on "Causality for FL."

Federated Causal Discovery (FCD)

The authors organize FCD methods along three axes:

Methodological Paradigm:
- Constraint-Based: Adaptations of PC and FCI algorithms (e.g., FedPC, FedC2SL) that perform federated conditional independence (CI) testing. These face challenges with error propagation and high-order CI test reliability in distributed settings.
- Score-Based: Methods (e.g., DARLS, FedGES) that optimize a global scoring criterion (like BIC) over DAG spaces or orderings. Challenges include super-exponential search spaces and sensitivity to local sample sizes.
- Continuous Optimization: Extensions of the NOTEARS framework (e.g., NOTEARS-ADMM, FedDAG) that reformulate DAG learning as a continuous program solvable via gradient-based distributed optimization. These face issues with non-convexity and high communication costs ( $O(d^2)$ ).
- Hybrid/Other: Methods combining paradigms or addressing specific settings like interventional data (FedCDI) or missing data (FedImpCSL).
Federation Topology:
- Horizontal: Clients share variables but have different samples (the dominant setting).
- Vertical: Clients share entities but have different variables (e.g., PP-BN(V), VertiBayes).
- Hybrid: Both samples and variables differ across clients.
Structural Scope:
- Global: Learning the full DAG over all variables.
- Local: Learning only the parents/children of a specific target variable (e.g., FedLCS).

Federated Causal Inference (FCI)

FCI methods are categorized by:

Target Estimand: Average Treatment Effect (ATE) vs. Individualized/Conditional Average Treatment Effects (ITE/CATE).
Estimation Strategy:
- Inverse Probability Weighting (IPW): Federated propensity score aggregation (e.g., FedIPW-MLE, Fed-IPW).
- Doubly Robust/Augmented: Methods like FedAIPW and FACE that combine outcome regression and propensity weighting for robustness.
- Matching: Federated propensity score matching (e.g., FPSM, MVAgg).
- Deep Generative/Transformers: Using VAEs and Transformers (e.g., FedTEDVAE, FedTransTEE) to learn representations, though these often lack formal theoretical guarantees.
- Specialized: Methods for survival analysis (FL-TTE), instrumental variables (FedIV), and double machine learning (FDML).

The Unified Pipeline

A core methodological contribution of the paper is the formalization of the connection between FCD and FCI. The authors propose a unified pipeline where FCD serves as an upstream stage to identify valid adjustment sets (via the back-door criterion) for FCI. They analyze the propagation of structural uncertainty (e.g., Markov Equivalence Class ambiguity) from the discovery stage to the inference stage, noting that naive point estimates can lead to overconfident conclusions.

3. Key Contributions

The paper claims the following contributions:

Comprehensive Scope: It offers the first dedicated, fine-grained survey of both FCD and FCI, moving beyond the broader "Causality for FL" perspective to focus on the core algorithmic challenges of distributed structure learning and effect estimation.
Novel Taxonomies: It introduces a three-axis taxonomy for FCD (Methodology $\times$ Topology $\times$ Scope) and a two-axis taxonomy for FCI (Estimand $\times$ Strategy), enabling principled comparisons across dimensions not previously synthesized.
Formalizing the Pipeline: It explicitly formalizes the dependency between FCD and FCI, analyzing how structural learning informs effect estimation and how errors propagate, a connection largely unexplored in prior literature.
Systematic Comparison: It provides detailed summary tables comparing methods based on privacy mechanisms, communication efficiency, theoretical guarantees, and handling of practical issues like heterogeneity and missing data.

4. Results and Analysis

The survey synthesizes findings from existing literature rather than presenting new experimental results. Key analytical observations include:

Dominance of Horizontal FL: Most existing work focuses on horizontal partitioning; vertical and hybrid settings remain significantly underexplored despite their practical relevance.
Handling Heterogeneity: While early methods assumed homogeneous data, recent works (e.g., FedDAG, FedCDH) have begun addressing heterogeneous causal mechanisms and non-identical variable sets.
Privacy Gaps: The majority of methods rely on the implicit assumption that not sharing raw data is sufficient for privacy. Only a few methods (e.g., PERI, I-PERI, Fed-Sparse-BNSL) provide formal differential privacy (DP) guarantees.
Communication Efficiency: Continuous optimization methods often incur high communication costs ( $O(d^2)$ ) due to matrix exchanges, whereas score-based and constraint-based methods vary widely.
Theoretical Limits: Convergence guarantees are scarce. Only a few methods (e.g., DARLS, FDBNL) offer formal convergence rates, and minimax rates for federated causal discovery under heterogeneity remain an open theoretical question.

5. Significance and Future Directions

The paper positions itself as a foundational reference for researchers entering the field of federated causal reasoning. Its significance lies in bridging the gap between the interdisciplinary fields of causal inference and federated learning, providing a structured framework to navigate the complex landscape of algorithms.

The authors identify several open challenges for future research:

Formal Privacy Guarantees: Developing tight composition theorems for multi-round causal protocols and characterizing the privacy-utility trade-off in structure learning.
Communication Efficiency: Designing protocols for high-dimensional settings, such as gradient compression and one-shot aggregation strategies.
Theoretical Foundations: Establishing finite-sample identifiability conditions, minimax rates, and semiparametric efficiency bounds for federated estimators.
Vertical and Hybrid Settings: Creating scalable protocols for settings where clients hold different variables.
Bridging Discovery and Inference: Developing end-to-end pipelines that jointly optimize structure learning and effect estimation, and methods to propagate structural uncertainty into effect estimates.
Complex Settings: Extending methods to handle latent confounders (PAGs), time-varying treatments, mediation analysis, and counterfactual reasoning.
Benchmarks: The field lacks standardized benchmarks; the authors call for community benchmarks with realistic heterogeneity, missing data, and ground-truth structures.

The paper concludes that while significant progress has been made, the field requires more rigorous theoretical foundations, standardized evaluation, and scalable solutions to realize the full potential of federated causal reasoning in domains like healthcare, economics, and engineering.