Learning causal graphs from observational data

Comprehending the causal relations between random variables is of paramount importance across various disciplines in science. The gold standard for uncovering causal connections is through Randomized Controlled Trials (RCTs). Nevertheless, practical constraints can render the execution of RCTs either infeasible or prohibitively expensive. In scenarios where RCTs cannot be applied, causal discovery techniques can be utilized to infer causal relations from observational data alone. In the thesis, I aim to identify several research gaps within the realm of causal discovery, and offer theoretical analysis and methodologies to address and resolve these issues. I present two works in the thesis. The first work is a nonparametric method that takes a temporal dataset as input and learns a dynamic Bayesian network capturing dependencies among the random variables across time steps. The second work is a parametric method assuming location-scale noise models. This method takes a static dataset as input and detects the cause random variable and the effect random variable from the data. Additionally, the work identifies the factors that impair the accuracy of maximum likelihood methods and provides a theoretical analysis to explain this phenomenon.