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 the same model architecture with the ELBO on sequential data.

But, they are limited to unimodal, Gaussian approximations of state uncertainty.

Most applications of machine learning to classification assume a closed set of balanced classes.

Thepartially observableMarkovdecision process (POMDP) provides ageneral framework for modeling an agent's decision process with state uncertainty, and online planning plays a pivotal role in solving it. A belief is a distribution of states representing state uncertainty. Methods forlarge-scale POMDP problems rely on the same idea of sampling both states and observations.

For challenging state estimation problems arising in domains like vision and robotics, particle-based representations attractively enable temporal reasoning aboutmultipleposteriormodes.

We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification.

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.

This paper is concerned with differentiable resampling in the context of sequential Monte Carlo (e.g., particle filtering). We propose a new informative resampling method that is instantly pathwise differentiable, based on an ensemble score diffusion model. We prove that our diffusion resampling method provides a consistent estimate to the resampling distribution, and we show by experiments that it outperforms the state-of-the-art differentiable resampling methods when used for stochastic filtering and parameter estimation.

We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a likelihood function is used for representing the measurement and its uncertainty. This likelihood is progressively introduced into the filtering procedure by homotopy continuation over an artificial time. A generalized Cramér distance between particle sets is derived in closed form that is differentiable and invariant to particle order. A Newton flow then continually minimizes this distance over artificial time and thus smoothly moves particles from prior to posterior density. The new filter is surprisingly simple to implement and very efficient. It just requires a prior particle set and a likelihood function, never estimates densities from samples, and can be used as a plugin replacement for classic approaches.