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Robust causal structure learning with some hidden variables
Author(s) -
Frot Benjamin,
Nandy Preetam,
Maathuis Marloes H.
Publication year - 2019
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12315
Subject(s) - directed acyclic graph , graphical model , hidden variable theory , causal structure , hidden markov model , hidden semi markov model , equivalence (formal languages) , class (philosophy) , rank (graph theory) , mathematics , computer science , graph , markov chain , artificial intelligence , markov model , algorithm , statistics , theoretical computer science , variable order markov model , combinatorics , discrete mathematics , physics , quantum mechanics , quantum
Summary We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so‐called low rank plus sparse framework, we suggest a two‐stage approach which first removes the effect of the hidden variables and then estimates the Markov equivalence class of the underlying DAG under the assumption that there are no remaining hidden variables. This approach is consistent in certain high dimensional regimes and performs favourably when compared with the state of the art, in terms of both graphical structure recovery and total causal effect estimation.