Sufficiency, Separability and Temporal Probabilistic Models
  Suppose we are given the conditional probability of one variable given some
other variables.Normally the full joint distribution over the conditioning
variablesis required to determine the probability of the conditioned
variable.Under what circumstances are the marginal distributions over the
conditioning variables sufficient to determine the probability ofthe
conditioned variable?Sufficiency in this sense is equivalent to additive
separability ofthe conditional probability distribution.Such separability
structure is natural and can be exploited forefficient inference.Separability
has a natural generalization to conditional separability.Separability provides
a precise notion of weaklyinteracting subsystems in temporal probabilistic
models.Given a system that is decomposed into separable subsystems,
exactmarginal probabilities over subsystems at future points in time can
becomputed by propagating marginal subsystem probabilities, rather thancomplete
system joint probabilities.Thus, separability can make exact prediction
tractable.However, observations can break separability,so exact monitoring of
dynamic systems remains hard.
