A Bayesian Approach to Constraint Based Causal Inference
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by
Tom Claassen, Tom Heskes
2012
Abstract
We target the problem of accuracy and robustness in causal inference from
finite data sets. Some state-of-the-art algorithms produce clear output
complete with solid theoretical guarantees but are susceptible to propagating
erroneous decisions, while others are very adept at handling and representing
uncertainty, but need to rely on undesirable assumptions. Our aim is to combine
the inherent robustness of the Bayesian approach with the theoretical strength
and clarity of constraint-based methods. We use a Bayesian score to obtain
probability estimates on the input statements used in a constraint-based
procedure. These are subsequently processed in decreasing order of reliability,
letting more reliable decisions take precedence in case of con icts, until a
single output model is obtained. Tests show that a basic implementation of the
resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already
outperforms established procedures such as FCI and Conservative PC. It can also
indicate which causal decisions in the output have high reliability and which
do not.
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