Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters
This addresses a technical bottleneck in parameter estimation for non-linear models using particle filters, offering incremental improvements in efficiency and accuracy for practitioners in fields like signal processing or machine learning.
The paper tackled the problem of non-differentiable resampling in particle filters by extending the reparameterisation trick to include stochastic inputs, enabling gradient calculations. This allowed the use of the No-U-Turn Sampler (NUTS) in particle Markov Chain Monte Carlo, which improved Markov chain mixing and produced more accurate results in less computational time compared to other methods.
It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The {\itshape reparameterisation trick} was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the {\itshape reparameterisation trick} to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider two state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time.