Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

Effective personalized incentives can improve user experience and increase platform revenue, resulting in a win-win situation between users and e-commerce companies. Previous studies have used uplift modeling methods to estimate the conditional average treatment effects of users' incentives, and then placed the incentives by maximizing the sum of estimated treatment effects under a limited budget. However, some users will always buy whether incentives are given or not, and they will actively collect and use incentives if provided, named "Always Buyers". Identifying and predicting these "Always Buyers" and reducing incentive delivery to them can lead to a more rational incentive allocation. In this paper, we first divide users into five strata from an individual counterfactual perspective, and reveal the failure of previous uplift modeling methods to identify and predict the "Always Buyers". Then, we propose principled counterfactual identification and estimation methods and prove their unbiasedness. We further propose a counterfactual entire-space multi-task learning approach to accurately perform personalized incentive policy learning with a limited budget. We also theoretically derive a lower bound on the reward of the learned policy. Extensive experiments are conducted on three real-world datasets with two common incentive scenarios, and the results demonstrate the effectiveness of the proposed approaches.

Causality plays a pivotal role in various fields of study. Based on the framework of causal graphical models, previous works have proposed identifying whether a variable is a cause or non-cause of another variable in every Markov equivalent graph by learning only the local structure. However, the presence of prior knowledge, often represented as a partially known causal graph, is common in many causal modeling applications. Leveraging this prior knowledge enables further identification of causal relations. In this paper, we first propose a method for learning the local structure by incorporating several types of causal background knowledge, including direct causal, non-ancestral, and ancestral information. Then we introduce sufficient and necessary conditions for identifying causal relations based solely on the local structure in the presence of prior knowledge. The effectiveness and efficiency of our method are demonstrated through experiments on local structure learning, causal relation identification, and its application to fair machine learning.