When used as a surrogate objective for maximum likelihood estimation in latent
variable models, the evidence lower bound (ELBO) produces state-of-the-art results.
Inspired by this, we consider the extension of the ELBO to a family of lower bounds
defined by a particle filter's estimator of the marginal likelihood, the filtering
variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can
exploit a model's sequential structure to form tighter bounds. We present results
that relate the tightness of FIVO's bound to the variance of the particle filter's
estimator by considering the generic case of bounds defined as log-transformed
likelihood estimators. Experimentally, we show that training with FIVO results in
substantial improvements over training with ELBO on sequential data.