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SUMMARY:Variable elimination and graph reduction: towards an efficient g-f
 ormula for causal DAGs - Richard Guo (University of Cambridge)
DTSTART:20211119T140000Z
DTEND:20211119T150000Z
UID:TALK162136@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Consider a study where the causal structure is known and descr
 ibed by a directed acyclic graph (DAG). A causal quantity of interest\, sa
 y a counterfactual mean\, can often be expressed as a functional of the ob
 served distribution given by the g-formula (also known as the "truncated f
 actorization"). The g-formula\, which can be written down from the graph\,
  usually takes the form of an integral involving conditional expectations 
 of the variables in the graph.\n\nNaturally\, to estimate the causal quant
 ity efficiently\, one can use a plugin estimator of the g-formula\, where 
 every conditional expectation is replaced by its MLE. However\, we find th
 at asymptotically not every variable appearing in the g-formula carries in
 formation for estimation. In fact\, the causal quantity can often be estim
 ated with an "efficient" g-formula that drops the redundant variables such
  that the cost of measuring these variables can be saved.\n\nWe present a 
 graphical procedure towards this goal. First\, we identify a set of graphi
 cal conditions that are necessary and sufficient for eliminating redundant
  variables. Second\, we construct a reduced DAG on the non-redundant varia
 bles only\, from which the "efficient" g-formula can be derived. The reduc
 ed DAG is transformed from the original DAG through a set of "moves"\, tra
 versing both within and between Markov equivalence classes\, which nonethe
 less preserve the semiparametric efficiency bound for estimating the causa
 l quantity.
LOCATION:MR12\, Centre for Mathematical Sciences
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