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CATEGORIES:Statistics
SUMMARY:Variable elimination and graph reduction: towards
an efficient g-formula for causal DAGs - Richard G
uo (University of Cambridge)
DTSTART;TZID=Europe/London:20211119T140000
DTEND;TZID=Europe/London:20211119T150000
UID:TALK162136AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/162136
DESCRIPTION:Consider a study where the causal structure is kno
wn and described by a directed acyclic graph (DAG)
. A causal quantity of interest\, say a counterfac
tual mean\, can often be expressed as a functional
of the observed distribution given by the g-formu
la (also known as the "truncated factorization").
The g-formula\, which can be written down from the
graph\, usually takes the form of an integral inv
olving conditional expectations of the variables i
n the graph.\n\nNaturally\, to estimate the causal
quantity efficiently\, one can use a plugin estim
ator of the g-formula\, where every conditional ex
pectation is replaced by its MLE. However\, we fin
d that asymptotically not every variable appearing
in the g-formula carries information for estimati
on. In fact\, the causal quantity can often be est
imated with an "efficient" g-formula that drops th
e redundant variables such that the cost of measur
ing these variables can be saved.\n\nWe present a
graphical procedure towards this goal. First\, we
identify a set of graphical conditions that are ne
cessary and sufficient for eliminating redundant v
ariables. Second\, we construct a reduced DAG on t
he non-redundant variables only\, from which the "
efficient" g-formula can be derived. The reduced D
AG is transformed from the original DAG through a
set of "moves"\, traversing both within and betwee
n Markov equivalence classes\, which nonetheless p
reserve the semiparametric efficiency bound for es
timating the causal quantity.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Qingyuan Zhao
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