Differentiable Particle Filtering using Optimal Placement Resampling
This work addresses a specific bottleneck in particle filtering for gradient-based learning, making it incremental but useful for researchers in state-space modeling.
The paper tackled the problem of nondifferentiability in particle filter-based loss functions for parameter estimation by proposing a differentiable resampling scheme using deterministic sampling from an empirical cumulative distribution function, resulting in improved performance on parameter inference and proposal learning tasks.
Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating the marginal data (observation) likelihood. A good proposal distribution and a good resampling scheme are crucial to obtain low variance estimates. However, traditional methods like multinomial resampling introduce nondifferentiability in PF-based loss functions for parameter estimation, prohibiting gradient-based learning tasks. This work proposes a differentiable resampling scheme by deterministic sampling from an empirical cumulative distribution function. We evaluate our method on parameter inference tasks and proposal learning.