2018/10/05 by Gunwoong Park, Park, Gunwoong, Sion Park +1 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1810.02501
43 pages
arxiv created 2019/05/27 · arxiv updated 2019/05/28
In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. 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 mean-variance relationship. We show that sample size n = Ω( d2 log9 p) is sufficient for our polynomial time Mean-variance 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.