text: Discovering causal relationships from observational data is a crucial problem and it has applications in many research areas. The PC algorithm is the state-of-the-art constraint based method for causal discovery. However, runtime of the PC algorithm, in the worst-case, is exponential to the number of nodes (variables), and thus it is inefficient when being applied to high dimensional data, e.g. gene expression datasets. On another note, the advancement of computer hardware in the last decade has resulted in the widespread availability of multi-core personal computers. There is a significant motivation for designing a parallelised PC algorithm that is suitable for personal computers and does not require end users’ parallel computing knowledge beyond their competency in using the PC algorithm. In this paper, we develop parallel-PC, a fast and memory efficient PC algorithm using the parallel computing technique. We apply our method to a range of synthetic and real-world high dimensional datasets. Experimental results on a dataset from the DREAM 5 challenge show that the original PC algorithm could not produce any results after running more than 24 hours; meanwhile, our parallel-PC algorithm managed to finish within around 12 hours with a 4-core CPU computer, and less than 6 hours with a 8-core CPU computer. Furthermore, we integrate parallel-PC into a causal inference method for inferring miRNA-mRNA regulatory relationships. The experimental results show that parallel-PC helps improve both the efficiency and accuracy of the causal inference algorithm.
  @cite_61: This brief presents four practical methods to effectively explore causal relationships, which are often used for explanation, prediction and decision making in medicine, epidemiology, biology, economics, physics and social sciences. The first two methods apply conditional independence tests for causal discovery. The last two methods employ association rule mining for efficient causal hypothesis generation, and a partial association test and retrospective cohort study for validating the hypotheses. All four methods are innovative and effective in identifying potential causal relationships around a given target, and each has its own strength and weakness. For each method, a software tool is provided along with examples demonstrating its use. Practical Approaches to Causal Relationship Exploration is designed for researchers and practitioners working in the areas of artificial intelligence, machine learning, data mining, and biomedical research. The material also benefits advanced students interested in causal relationship discovery.
  @cite_58: Discovering causal relationships in large databases of observational data is challenging. The pioneering work in this area was rooted in the theory of Bayesian network (BN) learning, which however, is a NP-complete problem. Hence several constraint-based algorithms have been developed to efficiently discover causations in large databases. These methods usually use the idea of BN learning, directly or indirectly, and are focused on causal relationships with single cause variables. In this paper, we propose an approach to mine causal rules in large databases of binary variables. Our method expands the scope of causality discovery to causal relationships with multiple cause variables, and we utilise partial association tests to exclude noncausal associations, to ensure the high reliability of discovered causal rules. Furthermore an efficient algorithm is designed for the tests in large databases. We assess the method with a set of real-world diagnostic data. The results show that our method can effectively discover interesting causal rules in large databases.
  @cite_4: Discovering causal relationships is the ultimate goal of many scientific explorations. Causal relationships can be identified with controlled experiments, but such experiments are often very expensive and sometimes impossible to conduct. On the other hand, the collection of observational data has increased dramatically in recent decades. Therefore it is desirable to find causal relationships from the data directly. Significant progress has been made in the field of discovering causal relationships using the Causal Bayesian Network (CBN) theory. The applications of CBNs, however, are greatly limited due to the high computational complexity. In another direction, association rule mining has been shown to be an efficient data mining means for relationship discovery. However, although causal relationships imply associations, the reverse does not always hold. In this paper we study how to use an efficient association mining approach to discover potential causal rules in observational data. We make use of the idea of retrospective cohort studies, a widely used approach in medical and social research, to detect causal association rules. In comparison with the constraint-based methods within the CBN paradigm, the proposed approach is faster and is capable of finding a cause consisting of combined variables.
  @cite_20: 
summary: In another direction, @cite_58 proposed an efficient method for testing the persistent associations between the target variable and its neighbours. The method is based on partial association tests and association rule mining framework to remove the spurious associations. In a similar fashion, @cite_4 @cite_20 integrated the ideas of retrospective cohort study with the association rule mining framework. They proposed to divide the samples into two groups of individuals, who share common characteristics but differ in regard to a certain factor of interest. The newly-designed dataset is called fair dataset" and is used to infer the level of influence that the factor of interest affects the target variable. These works were extended in @cite_61 , and the software tools were also provided. However, these methods are only applicable for binary datasets with a fixed target variable, and thus may not be suitable for high dimensional datasets, e.g. gene expression data.