  The lifted dynamic junction tree algorithm (LDJT) efficiently answers
filtering and prediction queries for probabilistic relational temporal models
by building and then reusing a first-order cluster representation of a
knowledge base for multiple queries and time steps. We extend LDJT to (i) solve
the smoothing inference problem to answer hindsight queries by introducing an
efficient backward pass and (ii) discuss different options to instantiate a
first-order cluster representation during a backward pass. Further, our
relational forward backward algorithm makes hindsight queries to the very
beginning feasible. LDJT answers multiple temporal queries faster than the
static lifted junction tree algorithm on an unrolled model, which performs
smoothing during message passing.
