Federated causal discovery aims to uncover causal relationships while protecting data privacy, with significant real-world applications. Existing methods focus on horizontal federated settings where clients share the same variables but have different samples. However, in practice, clients may have different variables, leading to spurious causal relationships. To address this issue, we comprehensively consider causal structure learning methods under both horizontal and vertical federated settings. Interestingly, we find that, higher-order cumulants rely solely on the joint distribution of the relevant variables and are useful to solve the above problem in the linear non-Gaussian case. This motivates us to provide the identification theories for determining the causal order over observed variables, leveraging the difference in the product of the (cross) cumulants of the specific variables. Based on these theories, we develop a method for learning causal order in the horizontal and vertical federated scenarios. Specifically, we first obtain local (cross) cumulant matrices of observed variables from all participating clients to construct a global cumulant matrix. This global cumulant matrix is then used for recursive source variable identification, ultimately yielding a causal strength matrix of the union of variables from all clients. Our algorithm demonstrates superior performance in experiments on both synthetic and real-world data.

Causal discovery plays a pivotal role in scientific inquiry and subsequent applications in prediction or decision-making. While many methods have been proposed, many of them rely on independence tests. However, these tests are difficult to implement and computationally intensive. In this article, we aim to propose a direct and computationally efficient method to determine the causal relationship between two observed variables in the linear non-Gaussian case. Building on the insight that cumulants provide information about the shape of a probability distribution, we show that interestingly, the (in)dependence between two observed variables can be directly inferred from the difference in the product of certain joint cumulants of these variables. This concept is named the cause difference criterion. Based on this criterion, we introduce two practical methods, high-order cumulant (HC) and HC-linear non-Gaussian acyclic model (LiNGAM), for causal discovery in the high-dimensional case. Theoretical analyses ensure the identifiability of the proposed criteria and methods. Experimental results indicate that our methods outperform most existing methods.

With the development of deep neural networks, deep reinforcement learning (DRL) has shown great potential in solving complex decision-making problems in high-dimensional environments. Among various DRL methods, Q-value function approaches are well-grounded in theory and exhibit strong practical performance, but often suffer from overestimation of the value function. We find that this overestimation primarily stems from unobserved random factors (latent variables) within the environmental dynamics, while existing solutions fail to address this issue, relying mainly on low-noise and unbiased sampling environments. To address this problem, we introduce latent variables to model unobserved randomness behind the environmental dynamics and employ causal models to capture the underlying data generation mechanisms. Subsequently, we propose a causal Q-value function method based on latent causal models. Specifically, we first design a causal encoding-decoding framework for learning the latent causal models, then utilize the inferred latent variables to construct a causal Q-value function, effectively mitigating the Q-value function overestimation problem. Experimental results show that our method significantly improves the stability of policy learning and the speed of convergence, enhancing the robustness of reinforcement learning in complex dynamic environments.

Causal discovery with latent variables is a crucial but challenging task. Despite the emergence of numerous methods aimed at addressing this challenge, they are not fully identified to the structure that two observed variables are influenced by one latent variable and there might be a directed edge in between. Interestingly, we notice that this structure can be identified through the utilization of higher-order cumulants. By leveraging the higher-order cumulants of non-Gaussian data, we provide an analytical solution for estimating the causal coefficients or their ratios. With the estimated (ratios of) causal coefficients, we propose a novel approach to identify the existence of a causal edge between two observed variables subject to latent variable influence. In case when such a causal edge exits, we introduce an asymmetry criterion to determine the causal direction. The experimental results demonstrate the effectiveness of our proposed method.

Learning Granger causality from event sequences is a challenging but essential task across various applications. Most existing methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.). However, this i.i.d. assumption is often violated due to the inherent dependencies among the event sequences. Fortunately, in practice, we find these dependencies can be modeled by a topological network, suggesting a potential solution to the non-i.i.d. problem by introducing the prior topological network into Granger causal discovery. This observation prompts us to tackle two ensuing challenges: 1) how to model the event sequences while incorporating both the prior topological network and the latent Granger causal structure, and 2) how to learn the Granger causal structure. To this end, we devise a unified topological neural Poisson auto-regressive model with two processes. In the generation process, we employ a variant of the neural Poisson process to model the event sequences, considering influences from both the topological network and the Granger causal structure. In the inference process, we formulate an amortized inference algorithm to infer the latent Granger causal structure. We encapsulate these two processes within a unified likelihood function, providing an end-to-end framework for this task. Experiments on simulated and real-world data demonstrate the effectiveness of our approach.

Causal discovery aims at revealing causal relations from observational data, which is a fundamental task in science and engineering. We describe causal-learn, an open-source Python library for causal discovery. This library focuses on bringing a comprehensive collection of causal discovery methods to both practitioners and researchers. It provides easy-to-use APIs for non-specialists, modular building blocks for developers, detailed documentation for learners, and comprehensive methods for all. Different from previous packages in R or Java, causal-learn is fully developed in Python, which could be more in tune with the recent preference shift in programming languages within related communities. The library is available at https://github.com/py-why/causal-learn.

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.

Localizing fault root causes is challenging but critical for wireless network operation and maintenance. Though supervised methods have shown promising results in training samples, most of the existing approaches assume that the training and the testing samples are independent and identical distributed. Such an i.i.d assumption usually does not hold due to network faults that may occur in different devices across different domains (well known as the distribution shift). Thus, it is necessary to align distributions between the training and test data set. Motivated by the stability of the causal mechanism across the domains, a Causal Alignment based Root Cause Localization (CARCL) framework, including the causal alignment and the multi-stage classifier, is proposed. CARCL first offers to align the distributions locally for each causal module but not globally on the complete variable set. We further develop a multi-stage classifier to determine the root causes with the help of predicted pseudo labels. The experiments demonstrate a superior performance of our method.

Over the past few years, we have made great progress in image categorization based on convolutional neural networks (CNNs). These CNNs are always trained based on a large-scale image data set; however, people may only have limited training samples for training CNN in the real-world applications. To solve this problem, one intuition is augmenting training samples. In this article, we propose an algorithm called Lavagan ( La tent V ariables A ugmentation Method based on G enerative A dversarial N ets) to improve the performance of CNN with insufficient training samples. The proposed Lavagan method is mainly composed of two tasks. The first task is that we augment a number latent variables (LVs) from a set of adaptive and constrained LVs distributions. In the second task, we take the augmented LVs into the training procedure of the image classifier. By taking these two tasks into account, we propose a uniform objective function to incorporate the two tasks into the learning. We then put forward an alternative two-play minimization game to minimize this uniform loss function such that we can obtain the predictive classifier. Moreover, based on Hoeffding’s Inequality and Chernoff Bounding method, we analyze the feasibility and efficiency of the proposed Lavagan method, which manifests that the LV augmentation method is able to improve the performance of Lavagan with insufficient training samples. Finally, the experiment has shown that the proposed Lavagan method is able to deliver more accurate performance than the existing state-of-the-art methods.

Causal discovery from observational data is a fundamental problem in science. Though the linear non-Gaussian acyclic model (LiNGAM) has shown promising results in various applications, it still faces the following challenges in the data with multiple latent confounders: 1) how to detect the latent confounders and 2) how to uncover the causal relations among observed and latent variables. To address these two challenges, we propose a hybrid causal discovery method for the LiNGAM with multiple latent confounders (MLCLiNGAM). First, we utilize the constraint-based method to learn the causal skeleton. Second, we identify the causal directions, by conducting regression and independence tests on the adjacent pairs in the causal skeleton. Third, we detect the latent confounders with the help of the maximal clique patterns raised by the latent confounders and reconstruct the causal structure with latent variables. Theoretical results show the correctness and efficiency of the algorithms. We conduct extensive experiments on synthetic and real data, which illustrates the efficiency and effectiveness of the proposed algorithms.

Domain adaptation on time series data is an important but challenging task. Most of the existing works in this area are based on the learning of the domain-invariant representation of the data with the help of restrictions like MMD. However, such extraction of the domain-invariant representation is a non-trivial task for time series data, due to the complex dependence among the timestamps. In detail, in the fully dependent time series, a small change of the time lags or the offsets may lead to difficulty in the domain invariant extraction. Fortunately, the stability of the causality inspired us to explore the domain invariant structure of the data. To reduce the difficulty in the discovery of causal structure, we relax it to the sparse associative structure and propose a novel sparse associative structure alignment model for domain adaptation. First, we generate the segment set to exclude the obstacle of offsets. Second, the intra-variables and inter-variables sparse attention mechanisms are devised to extract associative structure time-series data with considering time lags. Finally, the associative structure alignment is used to guide the transfer of knowledge from the source domain to the target one. Experimental studies not only verify the good performance of our methods on three real-world datasets but also provide some insightful discoveries on the transferred knowledge.

Understanding the causality behind the observational data is of great importance to a lot of real world applications, e.g., the improvement of Quality of Service. Non-Gaussianity has been exploited in numerous causal discovery methods for observational linear acyclic data. Transforming non-Gaussianity into indirect metrics is a conventional solution employed by existing methods, although this usually results in unreliable estimations or locally optimal solutions. In this work, we employs the excess kurtosis, a direct measure of non-Gaussianity, to establish a causal discovery method for linear non-Gaussian acyclic data. Firstly, we theoretically prove that an exogenous variable has the largest excess kurtosis when disturbance variables follow independent and identically distributions. Secondly, based on this property of exogenous variables, we propose an efficient exogenous variable identification algorithm, and develop a causal discovery method. Extensive experiment results verify the effectiveness and efficiency of the proposed approach.