Conventional causal discovery methods rely on centralized data, which is
inconsistent with the decentralized nature of data in many real-world
situations. This discrepancy has motivated the development of federated causal
discovery (FCD) approaches. However, existing FCD methods may be limited by
their potentially restrictive assumptions of identifiable functional causal
models or homogeneous data distributions, narrowing their applicability in
diverse scenarios. In this paper, we propose a novel FCD method attempting to
accommodate arbitrary causal models and heterogeneous data. We first utilize a
surrogate variable corresponding to the client index to account for the data
heterogeneity across different clients. We then develop a federated conditional
independence test (FCIT) for causal skeleton discovery and establish a
federated independent change principle (FICP) to determine causal directions.
These approaches involve constructing summary statistics as a proxy of the raw
data to protect data privacy. Owing to the nonparametric properties, FCIT and
FICP make no assumption about particular functional forms, thereby facilitating
the handling of arbitrary causal models. We conduct extensive experiments on
synthetic and real datasets to show the efficacy of our method. The code is
available at https://github.com/lokali/FedCDH.git.

提出了一种新的面向任意因果模型和异构数据的联邦因果探索方法，通过使用代理变量来解决不同客户端之间的数据异构性，并利用联邦条件独立性检验和联邦独立性改变原则来确定因果方向，无需对特定函数形式进行任何假设，以以保护数据隐私的方式构建摘要统计量，实验证明了该方法的有效性。

异构数据的联邦因果推断

Federated Causal Discovery from Heterogeneous Data

Understanding causal relations is vital in scientific discovery. The process
of causal structure learning involves identifying causal graphs from
observational data to understand such relations. Usually, a central server
performs this task, but sharing data with the server poses privacy risks.
Federated learning can solve this problem, but existing solutions for federated
causal structure learning make unrealistic assumptions about data and lack
convergence guarantees. FedC2SL is a federated constraint-based causal
structure learning scheme that learns causal graphs using a federated
conditional independence test, which examines conditional independence between
two variables under a condition set without collecting raw data from clients.
FedC2SL requires weaker and more realistic assumptions about data and offers
stronger resistance to data variability among clients. FedPC and FedFCI are the
two variants of FedC2SL for causal structure learning in causal sufficiency and
causal insufficiency, respectively. The study evaluates FedC2SL using both
synthetic datasets and real-world data against existing solutions and finds it
demonstrates encouraging performance and strong resilience to data
heterogeneity among clients.

本研究提出了一个名为 FedC2SL 的联邦约束因果结构学习方案，它使用联邦有条件独立性检验学习因果图，该方案需要更弱和更现实的数据假设，并针对客户端数据变异提供更强的抗性，从而解决了在保护隐私方面存在的一些问题。实验结果表明，FedC2SL 具有令人鼓舞的性能和对客户端数据异质性的强大韧性。

实现可行的联邦因果结构学习

Towards Practical Federated Causal Structure Learning

We give a new consistent scoring function for structure learning of Bayesian
networks. In contrast to traditional approaches to scorebased structure
learning, such as BDeu or MDL, the complexity penalty that we propose is
data-dependent and is given by the probability that a conditional independence
test correctly shows that an edge cannot exist. What really distinguishes this
new scoring function from earlier work is that it has the property of becoming
computationally easier to maximize as the amount of data increases. We prove a
polynomial sample complexity result, showing that maximizing this score is
guaranteed to correctly learn a structure with no false edges and a
distribution close to the generating distribution, whenever there exists a
Bayesian network which is a perfect map for the data generating distribution.
Although the new score can be used with any search algorithm, we give empirical
results showing that it is particularly effective when used together with a
linear programming relaxation approach to Bayesian network structure learning.

本文提出了一种新的一致性结构学习评分函数，与传统方法相比，该评分函数具有数据相关性且随着数据量的增加而变得更易于最大化，使用线性规划松弛方法时效果特别好，可学习与生成分布接近且没有错误边的结构。