  Learning generative models and inferring latent trajectories have shown to be
challenging for time series due to the intractable marginal likelihoods of
flexible generative models. It can be addressed by surrogate objectives for
optimization. We propose Monte Carlo filtering objectives (MCFOs), a family of
variational objectives for jointly learning parametric generative models and
amortized adaptive importance proposals of time series. MCFOs extend the
choices of likelihood estimators beyond Sequential Monte Carlo in
state-of-the-art objectives, possess important properties revealing the factors
for the tightness of objectives, and allow for less biased and variant gradient
estimates. We demonstrate that the proposed MCFOs and gradient estimations lead
to efficient and stable model learning, and learned generative models well
explain data and importance proposals are more sample efficient on various
kinds of time series data.
