  Variational inference for state space models (SSMs) is known to be hard in
general. Recent works focus on deriving variational objectives for SSMs from
unbiased sequential Monte Carlo estimators. We reveal that the marginal
particle filter is obtained from sequential Monte Carlo by applying
Rao-Blackwellization operations, which sacrifices the trajectory information
for reduced variance and differentiability. We propose the variational marginal
particle filter (VMPF), which is a differentiable and reparameterizable
variational filtering objective for SSMs based on an unbiased estimator. We
find that VMPF with biased gradients gives tighter bounds than previous
objectives, and the unbiased reparameterization gradients are sometimes
beneficial.
