Differentiable and Stable Long-Range Tracking of Multiple Posterior
  Modes
Ali Younis Erik Sudderth
Particle filters flexibly represent multiple posterior modes
nonparametrically, via a collection of weighted samples, but have classically
been applied to tracking problems with known dynamics and observation
likelihoods. Such generative models may be inaccurate or unavailable for
high-dimensional observations like images. We instead leverage training data to
discriminatively learn particle-based representations of uncertainty in latent
object states, conditioned on arbitrary observations via deep neural network
encoders. While prior discriminative particle filters have used heuristic
relaxations of discrete particle resampling, or biased learning by truncating
gradients at resampling steps, we achieve unbiased and low-variance gradient
estimates by representing posteriors as continuous mixture densities. Our
theory and experiments expose dramatic failures of existing
reparameterization-based estimators for mixture gradients, an issue we address
via an importance-sampling gradient estimator. Unlike standard recurrent neural
networks, our mixture density particle filter represents multimodal uncertainty
in continuous latent states, improving accuracy and robustness. On a range of
challenging tracking and robot localization problems, our approach achieves
dramatic improvements in accuracy, while also showing much greater stability
across multiple training runs.