Causal Discovery (CD) is the process of identifying the cause-effect relationships among the variables of a system from data. Over the years, several methods have been developed primarily based on the statistical properties of data to uncover the underlying causal mechanism. In this study, we present an extensive discussion on the methods designed to perform causal discovery from both independent and identically distributed (i.i.d.) data and time series data. For this purpose, we first introduce the common terminologies in causal discovery, and then provide a comprehensive discussion of the algorithms designed to identify the causal edges in different settings. We further discuss some of the benchmark datasets available for evaluating the performance of the causal discovery methods, available tools or software packages to perform causal discovery readily, and the common metrics used to evaluate these methods. We also test some common causal discovery algorithms on different benchmark datasets, and compare their performances. Finally, we conclude by presenting the common challenges involved in causal discovery, and also, discuss the applications of causal discovery in multiple areas of interest.
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