Title: Uncovering hidden causality from noisy complex data

Abstract: Understanding how variables causally influence each other is fundamental across scientific fields, yet many real-world datasets are both noisy and complex, posing challenges to standard causal analysis tools. In this talk, I will present two projects that address underexplored causal effects in such settings. In the first part, I focus on causal discovery with heteroscedastic errors. I introduce the Residual Quantile Estimation (ResQuE) algorithm, designed to learn Directed Acyclic Graphs (DAGs) by explicitly modeling non-constant error variances. ResQuE iteratively reconstructs causal order while balancing efficiency and robustness. I will then discuss its theoretical guarantees and empirical results on benchmark datasets that highlight its ability to detect additional causal heteroscedasticity effects. In the second part, I will introduce a new variance-based mediation analysis framework aimed at quantifying the overall contribution of high-dimensional omics mediators with weak effects, a setting often overlooked by existing methods. Using a mixed-effects working model, we develop a flexible and computationally efficient estimation procedure. Applying this approach to the Multi-ethnic study of atherosclerosis (MESA) data reveals that a considerable portion of the mediation effect is likely driven by weak mediators that traditional methods tend to misestimate. I will conclude by discussing broader methodological extensions and future directions, emphasizing how these new perspectives can enrich both theoretical and applied research in causal inference.