This paper investigates the problem of selecting instrumental variables relative to a target causal influence $X\to Y$ from observational data generated by linear non-Gaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear non-Gaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method.

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.

This paper addresses the challenge of identifying causes for functional dynamic targets, which are functions of various variables over time. We develop screening and local learning methods to learn the direct causes of the target, as well as all indirect causes up to a given distance. We first discuss the modeling of the functional dynamic target. Then, we propose a screening method to select the variables that are significantly correlated with the target. On this basis, we introduce an algorithm that combines screening and structural learning techniques to uncover the causal structure among the target and its causes. To tackle the distance effect, where long causal paths weaken correlation, we propose a local method to discover the direct causes of the target in these significant variables and further sequentially find all indirect causes up to a given distance. We show theoretically that our proposed methods can learn the causes correctly under some regular assumptions. Experiments based on synthetic data also show that the proposed methods perform well in learning the causes of the target.

In this paper, we discuss structure learning of causal networks from multiple data sets obtained by external intervention experiments where we do not know what variables are manipulated. For example, the conditions in these experiments are changed by changing temperature or using drugs, but we do not know what target variables are manipulated by the external interventions. From such data sets, the structure learning becomes more difficult. For this case, we first discuss the identifiability of causal structures. Next we present a graph-merging method for learning causal networks for the case that the sample sizes are large for these interventions. Then for the case that the sample sizes of these interventions are relatively small, we propose a data-pooling method for learning causal networks in which we pool all data sets of these interventions together for the learning. Further we propose a re-sampling approach to evaluate the edges of the causal network learned by the data-pooling method. Finally we illustrate the proposed learning methods by simulations.