For challenging state estimation problems arising in domains like vision and robotics, particle-based representations attractively enable temporal reasoning about multiple posterior modes. Particle smoothers offer the potential for more accurate offline data analysis by propagating information both forward and backward in time, but have classically required human-engineered dynamics and observation models. Extending recent advances in discriminative training of particle filters, we develop a framework for low-variance propagation of gradients across long time sequences when training particle smoothers. Our "two-filter" smoother integrates particle streams that are propagated forward and backward in time, while incorporating stratification and importance weights in the resampling step to provide low-variance gradient estimates for neural network dynamics and observation models. The resulting mixture density particle smoother is substantially more accurate than state-of-the-art particle filters, as well as search-based baselines, for city-scale global vehicle localization from real-world videos and maps.

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, will also showing much greater stability across multiple training runs.

Deep generative models like variational autoencoders (VAEs) are widely used for density estimation and dimensionality reduction, but infer latent representations via amortized inference algorithms, which require that all data dimensions are observed. VAEs thus lack a key strength of probabilistic graphical models: the ability to infer posteriors for test queries with arbitrary structure. We demonstrate that many prior methods for imputation with VAEs are costly and ineffective, and achieve superior performance via query-adaptive variational inference (QAVI) algorithms based directly on the generative decoder. By analytically marginalizing arbitrary sets of missing features, and optimizing expressive posteriors including mixtures and density flows, our non-amortized QAVI algorithms achieve excellent performance while avoiding expensive model retraining. On standard image and tabular datasets, our approach substantially outperforms prior methods in the plausibility and diversity of imputations. We also show that QAVI effectively generalizes to recent hierarchical VAE models for high-dimensional images.