Novel Ordering-Based Approaches for Causal Structure Learning in the Presence of Unobserved Variables
Ehsan Mokhtarian, Mohmmadsadegh Khorasani, Jalal Etesami, Negar Kiyavash
Abstract
We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature recover a graph through learning a causal order (c-order). We advocate for a novel order called removable order (r-order) as they are advantageous over c-orders for structure learning. This is because r-orders are the minimizers of an appropriately defined optimization problem that could be either solved exactly (using a reinforcement learning approach) or approximately (using a hill-climbing search). Moreover, the r-orders (unlike c-orders) are invariant among all the graphs in a MEC and include c-orders as a subset. Given that set of r-orders is often significantly larger than the set of c-orders, it is easier for the optimization problem to find an r-order instead of a c-order. We evaluate the performance and the scalability of our proposed approaches on both real-world and randomly generated networks.
BibTeX
@article{Mokhtarian_Khorasani_Etesami_Kiyavash_2023, title={Novel Ordering-Based Approaches for Causal Structure Learning in the Presence of Unobserved Variables}, volume={37}, url={https://ojs.aaai.org/index.php/AAAI/article/view/26445}, DOI={10.1609/aaai.v37i10.26445}, abstractNote={We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature recover a graph through learning a causal order (c-order). We advocate for a novel order called removable order (r-order) as they are advantageous over c-orders for structure learning. This is because r-orders are the minimizers of an appropriately defined optimization problem that could be either solved exactly (using a reinforcement learning approach) or approximately (using a hill-climbing search). Moreover, the r-orders (unlike c-orders) are invariant among all the graphs in a MEC and include c-orders as a subset. Given that set of r-orders is often significantly larger than the set of c-orders, it is easier for the optimization problem to find an r-order instead of a c-order. We evaluate the performance and the scalability of our proposed approaches on both real-world and randomly generated networks.}, number={10}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Mokhtarian, Ehsan and Khorasani, Mohmmadsadegh and Etesami, Jalal and Kiyavash, Negar}, year={2023}, month={Jun.}, pages={12260-12268} }