Publication
Understanding how changes in an environment affect outcomes is at the core of causal inference. Unlike standard prediction tasks that capture associations between variables, causal inference aims to reveal what happens when we intervene in a system. In this field, there is a common pipeline consisting of two main problems: causal discovery and causal effect identification. Rather than learning the exact functions among variables, causal discovery focuses on learning a causal graph that shows which variables directly influence others. Once such a graph is obtainedâ either partially or fullyâ the goal of causal effect identification is to use this structural information, along with the available observational data, to compute the effect of interventions. In this thesis, we contribute to various parts of this pipeline. First, we introduce a recursive framework for observational causal discovery. This framework significantly reduces the computational complexity of the problem and improves learning accuracy in practice when sample sizes are limited and statistical tests are noisy. Following this framework, we propose several methods, each designed under different sets of assumptions. We also present an approach that speeds up existing permutation-based methods. However, causal discovery from observational data alone cannot uniquely determine the causal graph, and the problem becomes even more challenging when the graph is cyclic. In these cases, the gold standard is to perform interventions. In the second part of the thesis, we address interventional causal discovery in cyclic graphs by deriving lower bounds that illustrate the complexity of the problem and proposing methods under different assumptions that nearly match these bounds. In the third part, we focus on a crucial causal effect identification problem known as s-ID, which aims to identify the causal effects within a specific sub-population using observational data from that sub-population. We formalize the s-ID problem and propose a sound and complete algorithm under appropriate assumptions. In addition to these contributions, we briefly discuss other contributions that we have made according to the aforementioned pipeline in the introduction.