High-Dimensional Poisson Structural Equation Model Learning via ℓ1-Regularized Regression
Gunwoong Park, Sion Park; 20(95):1−41, 2019.
Abstract
In this paper, we develop a new approach to learning high-dimensional Poisson structural equation models from only observational data without strong assumptions such as faithfulness and a sparse moralized graph. A key component of our method is to decouple the ordering estimation or parent search where the problems can be efficiently addressed using ℓ1-regularized regression and the moments relation. We show that sample size n=Ω(d2log9p) is sufficient for our polynomial time Moments Ratio Scoring (MRS) algorithm to recover the true directed graph, where p is the number of nodes and d is the maximum indegree. We verify through simulations that our algorithm is statistically consistent in the high-dimensional p>n setting, and performs well compared to state-of-the-art ODS, GES, and MMHC algorithms. We also demonstrate through multivariate real count data that our MRS algorithm is well-suited to estimating DAG models for multivariate count data in comparison to other methods used for discrete data.
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