35,324 research outputs found
SDDs are Exponentially More Succinct than OBDDs
Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are
essentially as tractable as ordered binary decision diagrams (OBDDs), but tend
to be more succinct in practice. This makes SDDs a prominent representation
language, with many applications in artificial intelligence and knowledge
compilation. We prove that SDDs are more succinct than OBDDs also in theory, by
constructing a family of boolean functions where each member has polynomial SDD
size but exponential OBDD size. This exponential separation improves a
quasipolynomial separation recently established by Razgon (2013), and settles
an open problem in knowledge compilation
Graphical Models for Inference Under Outcome-Dependent Sampling
We consider situations where data have been collected such that the sampling
depends on the outcome of interest and possibly further covariates, as for
instance in case-control studies. Graphical models represent assumptions about
the conditional independencies among the variables. By including a node for the
sampling indicator, assumptions about sampling processes can be made explicit.
We demonstrate how to read off such graphs whether consistent estimation of the
association between exposure and outcome is possible. Moreover, we give
sufficient graphical conditions for testing and estimating the causal effect of
exposure on outcome. The practical use is illustrated with a number of
examples.Comment: Published in at http://dx.doi.org/10.1214/10-STS340 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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