  Sequential Monte Carlo (SMC) is an inference algorithm for state space models
that approximates the posterior by sampling from a sequence of target
distributions. The target distributions are often chosen to be the filtering
distributions, but these ignore information from future observations, leading
to practical and theoretical limitations in inference and model learning. We
introduce SIXO, a method that instead learns targets that approximate the
smoothing distributions, incorporating information from all observations. The
key idea is to use density ratio estimation to fit functions that warp the
filtering distributions into the smoothing distributions. We then use SMC with
these learned targets to define a variational objective for model and proposal
learning. SIXO yields provably tighter log marginal lower bounds and offers
significantly more accurate posterior inferences and parameter estimates in a
variety of domains.
