Constraint-based methods and noise-based methods are two distinct families of methods proposed for uncovering causal graphs from observational data. However, both operate under strong assumptions that may be challenging to validate or could be violated in real-world scenarios. In response to these challenges, there is a growing interest in hybrid methods that amalgamate principles from both methods, showing robustness to assumption violations. This paper introduces a novel comprehensive framework for hybridizing constraint-based and noise-based methods designed to uncover causal graphs from observational time series. The framework is structured into two classes. The first class employs a noise-based strategy to identify a super graph, containing the true graph, followed by a constraint-based strategy to eliminate unnecessary edges. In the second class, a constraint-based strategy is applied to identify a skeleton, which is then oriented using a noise-based strategy. The paper provides theoretical guarantees for each class under the condition that all assumptions are satisfied, and it outlines some properties when assumptions are violated. To validate the efficacy of the framework, two algorithms from each class are experimentally tested on simulated data, realistic ecological data, and real datasets sourced from diverse applications. Notably, two novel datasets related to Information Technology monitoring are introduced within the set of considered real datasets. The experimental results underscore the robustness and effectiveness of the hybrid approaches across a broad spectrum of datasets.

翻译：约束方法和噪声方法是从观测数据中发现因果图的两类不同方法。然而，两者都在较强假设下运行，这些假设在实际场景中可能难以验证甚至被违反。为应对这些挑战，融合两类方法原理的混合方法日益受到关注，展现出对假设违背的鲁棒性。本文提出一种新颖的综合性框架，用于混合约束方法和噪声方法，旨在从观测时间序列中发现因果图。该框架分为两类：第一类采用噪声导向策略识别包含真实图的超图，随后通过约束导向策略移除冗余边；第二类则先通过约束导向策略识别骨架，再基于噪声导向策略确定方向。在假设全部满足的条件下，本文为每一类方法提供了理论保证，并阐述了假设违背时的一些特性。为验证框架有效性，我们针对每类方法各设计了两种算法，并在模拟数据、真实生态数据及来自不同应用领域的真实数据集上进行了实验测试。特别地，在所考虑的真实数据集中引入了两个与信息技术监控相关的新数据集。实验结果充分证明了混合方法在广泛数据集上的鲁棒性和有效性。