New method finds causal relationships in complex data with optimization
MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimization
Machine Learning
Summary
Understanding cause-and-effect in data is challenging, especially when data errors don’t follow simple patterns. The authors developed a new approach called MARCEDES that looks for the best explanation of how data variables influence one another using math and optimization techniques. Their method works well even when data is complex and comes in large amounts, by cleverly simplifying the search for these relationships. They show that MARCEDES can find true cause-effect structures more accurately than existing methods through detailed testing.
What this means in practice
- •For data science teams: Identify accurate cause-effect links in complex datasets for better decision-making models.
- •For machine learning engineers: Improve model structure learning involving non-standard noise distributions using efficient continuous optimization.
Authors
Anamitra Chaudhuri, Anirban Bhattacharya, Yang Ni
Abstract
We consider the problem of learning the underlying causal directed acyclic graph (DAG) structure corresponding to a structural equation model (SEM) with non-Gaussian errors. Motivated by an intentionally misspecified non-Gaussian SEM with all Laplace errors, we first introduce the mean absolute residual risk, defined over the space of all real matrices, and show that, asymptotically, the risk of the true weighted causal DAG matrix is strictly smaller than that of any other matrix. Nevertheless, to enhance generality and account for high-dimensional and finite-sample settings, we further incorporate row-specific sparsity penalties along with a soft DAG constraint to derive a continuous score function over the space of real matrices. Accordingly, we propose a score-based DAG learning method, named MARCEDES, formulated as an unconstrained score minimization problem, which can be efficiently solved using gradient-based optimization techniques, thereby circumventing the challenges associated with constrained optimization. Furthermore, we develop a computational algorithm to handle the non-smoothness of the score objective and to enable optimal tuning of row-specific sparsity penalties under a generalized Bayes framework. Finally, we demonstrate the efficiency and improved performance of the proposed method over existing approaches through an extensive simulation study.