Causality plays a pivotal role in various fields of study. Based on the framework of causal graphical models, previous works have proposed identifying whether a variable is a cause or non-cause of another variable in every Markov equivalent graph by learning only the local structure. However, the presence of prior knowledge, often represented as a partially known causal graph, is common in many causal modeling applications. Leveraging this prior knowledge enables further identification of causal relations. In this paper, we first propose a method for learning the local structure by incorporating several types of causal background knowledge, including direct causal, non-ancestral, and ancestral information. Then we introduce sufficient and necessary conditions for identifying causal relations based solely on the local structure in the presence of prior knowledge. The effectiveness and efficiency of our method are demonstrated through experiments on local structure learning, causal relation identification, and its application to fair machine learning.

Pairwise causal background knowledge about the existence or absence of causal edges and paths is frequently encountered in observational studies. Such constraints allow the shared directed and undirected edges in the constrained subclass of Markov equivalent DAGs to be represented as a causal maximally partially directed acyclic graph (MPDAG). In this paper, we first provide a sound and complete graphical characterization of causal MPDAGs and introduce a minimal representation of a causal MPDAG. Then, we give a unified representation for three types of pairwise causal background knowledge, including direct, ancestral and non-ancestral causal knowledge, by introducing a novel concept called direct causal clause (DCC). Using DCCs, we study the consistency and equivalence of pairwise causal background knowledge and show that any pairwise causal background knowledge set can be uniquely and equivalently decomposed into the causal MPDAG representing the refined Markov equivalence class and a minimal residual set of DCCs. Polynomial-time algorithms are also provided for checking consistency and equivalence, as well as for finding the decomposed MPDAG and the residual DCCs. Finally, with pairwise causal background knowledge, we prove a sufficient and necessary condition to identify causal effects and surprisingly find that the identifiability of causal effects only depends on the decomposed MPDAG. We also develop a local IDA-type algorithm to estimate the possible values of an unidentifiable effect. Simulations suggest that pairwise causal background knowledge can significantly improve the identifiability of causal effects.

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

Identifying the causes of an event, also termed as causal attribution, is a commonly encountered task in many application problems. Available methods, mostly in Bayesian or causal inference literature, suffer from two main drawbacks: 1) cannot attribute for individuals, and 2) attributing one single cause at a time and cannot deal with the interaction effect among multiple causes. In this paper, based on our proposed new measurement, called conditional counterfactual causal effect (CCCE), we introduce an individual causal attribution method, which is able to utilize the individual observation as the evidence and consider common influence and interaction effect of multiple causes simultaneously. We discuss the identifiability of CCCE and also give the identification formulas under proper assumptions. Finally, we conduct experiments on simulated and real data to illustrate the effectiveness of CCCE and the results show that our proposed method outperforms significantly state-of-the-art methods.

Traditional causal discovery methods mainly focus on estimating causal relations among measured variables, but in many real-world problems, such as questionnaire-based psychometric studies, measured variables are generated by latent variables that are causally related. Accordingly, this paper investigates the problem of discovering the hidden causal variables and estimating the causal structure, including both the causal relations among latent variables and those between latent and measured variables. We relax the frequently-used measurement assumption and allow the children of latent variables to be latent as well, and hence deal with a specific type of latent hierarchical causal structure. In particular, we define a minimal latent hierarchical structure and show that for linear non-Gaussian models with the minimal latent hierarchical structure, the whole structure is identifiable from only the measured variables. Moreover, we develop a principled method to identify the structure by testing for Generalized Independent Noise (GIN) conditions in specific ways. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.

In this paper, we consider the problem of estimating all possible causal effects from observational data with two types of background knowledge: direct causal information and non-ancestral information. Following the IDA framework, we first provide locally valid orientation rules for maximal partially directed acyclic graphs (PDAGs), which are widely used to represent background knowledge. Based on the proposed rules, we present a fully local algorithm to estimate all possible causal effects with direct causal information. Furthermore, we consider non-ancestral information and prove that it can be equivalently transformed into direct causal information, meaning that we can also locally estimate all possible causal effects with non-ancestral information. The test results on both synthetic and real-world data sets show that our methods are efficient and stable.

It is clear that some causal effects cannot be identified from observational data when the causal directed acyclic graph is absent. In such cases, IDA is a useful framework which estimates all possible causal effects by adjusting for all possible parental sets. In this paper, we combine the adjustment set selection procedure with the original IDA framework. Our goal is to find a common set that can be subtracted from all possible parental sets without influencing the back-door adjustment. To this end, we first introduce graphical conditions to decide whether a treatment’s neighbor or parent in a completed partially directed acyclic graph (CPDAG) can be subtracted and then provide a procedure to construct a subtractable set from those subtractable vertices. We next combine the procedure with the IDA framework and provide a fully local modification of IDA. Experimental results show that, with our modification, both the number of possible parental sets and the size of each possible parental set enumerated by the modified IDA decrease, making it possible to estimate all possible causal effects more efficiently.

In observational studies, it is important to evaluate not only the total effect but also the direct and indirect effects of a treatment variable on a response variable. In terms of local structural learning of causal networks, we try to find all possible pairs of total and direct causal effects, which can further be used to calculate indirect causal effects. An intuitive global learning approach is first to find an essential graph over all variables representing all Markov equivalent causal networks, and then enumerate all equivalent networks and estimate a pair of the total and direct effects for each of them. However, it could be inefficient to learn an essential graph and enumerate equivalent networks when the true causal graph is large. In this paper, we propose a local learning approach instead. In the local learning approach, we first learn locally a chain component containing the treatment. Then, if necessary, we learn locally a chain component containing the response. Next, we locally enumerate all possible pairs of the treatment's parents and the response's parents. Finally based on these pairs, we find all possible pairs of total and direct effects of the treatment on the response.