---
res:
bibo_abstract:
- We consider the problem of learning a Bayesian network or directed acyclic graph
model from observational data. A number of constraint‐based, score‐based and hybrid
algorithms have been developed for this purpose. Statistical consistency guarantees
of these algorithms rely on the faithfulness assumption, which has been shown
to be restrictive especially for graphs with cycles in the skeleton. We here propose
the sparsest permutation (SP) algorithm, showing that learning Bayesian networks
is possible under strictly weaker assumptions than faithfulness. This comes at
a computational price, thereby indicating a statistical‐computational trade‐off
for causal inference algorithms. In the Gaussian noiseless setting, we prove that
the SP algorithm boils down to finding the permutation of the variables with the
sparsest Cholesky decomposition of the inverse covariance matrix, which is equivalent
to ℓ0‐penalized maximum likelihood estimation. We end with a simulation study
showing that in line with the proven stronger consistency guarantees, and the
SP algorithm compares favourably to standard causal inference algorithms in terms
of accuracy for a given sample size.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Garvesh
foaf_name: Raskutti, Garvesh
foaf_surname: Raskutti
- foaf_Person:
foaf_givenName: Caroline
foaf_name: Uhler, Caroline
foaf_surname: Uhler
foaf_workInfoHomepage: http://www.librecat.org/personId=49ADD78E-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-7008-0216
bibo_doi: 10.1002/sta4.183
bibo_issue: '1'
bibo_volume: 7
dct_date: 2018^xs_gYear
dct_language: eng
dct_publisher: Wiley@
dct_title: Learning directed acyclic graphs based on sparsest permutations@
...