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Particle Rejuvenation

To increase particle diversity (e.g. after a resampling step), GenParticleFilters.jl provides support for both MCMC and move-reweight rejuvenation kernels.

GenParticleFilters.pf_rejuvenate! — Function
pf_rejuvenate!(state::ParticleFilterState, kern, kern_args::Tuple=(),
               n_iters::Int=1; method=:move, kwargs...)

Rejuvenates particles by repeated application of a kernel kern. kern should be a callable which takes a trace as its first argument, and returns a tuple with a trace as the first return value. method specifies the rejuvenation method: :move for MCMC moves without a reweighting step, and :reweight for rejuvenation with a reweighting step. Additional keyword arguments are passed to the kernel.

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MCMC rejuvenation

MCMC rejuvenation can be used to diversify the set of existing particles by applying an invariant MCMC kernel (e.g. a Metropolis-Hastings kernel) to each particle. Since the kernel is expected to be invariant, kernel application does not adjust the particle weights.

GenParticleFilters.pf_move_accept! — Function
pf_move_accept!(state::ParticleFilterState, kern,
                kern_args::Tuple=(), n_iters::Int=1; kwargs...)

Rejuvenates particles by repeated application of a MCMC kernel kern. kern should be a callable which takes a trace as its first argument, and returns a tuple (trace, accept), where trace is the (potentially) new trace, and accept is true if the MCMC move was accepted. Subsequent arguments to kern can be supplied with kern_args or kwargs. The kernel is repeatedly applied to each trace for n_iters.

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Move-reweight rejuvenation

Move-reweight rejuvenation can be used to simultaneously diversify the set of existing particles while updating their weights.

GenParticleFilters.pf_move_reweight! — Function
pf_move_reweight!(state::ParticleFilterState, kern,
                  kern_args::Tuple=(), n_iters::Int=1; kwargs...)

Rejuvenates and reweights particles by repeated application of a reweighting kernel kern, as described in [1]. kern should be a callable which takes a trace as its first argument, and returns a tuple (trace, rel_weight), where trace is the new trace, and rel_weight is the relative log-importance weight. Subsequent arguments to kern can be supplied with kern_args or kwargs. The kernel is repeatedly applied to each trace for n_iters, and the weights accumulated accordingly.

Both the move_reweight function and symmetric trace translators can serve as reweighting kernels.

[1] R. A. G. Marques and G. Storvik, "Particle move-reweighting strategies for online inference," Preprint series. Statistical Research Report, 2013.

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To define a move-reweight kernel, the following methods are provided:

GenParticleFilters.move_reweight — Function
move_reweight(trace, selection; kwargs...)
move_reweight(trace, proposal, proposal_args; kwargs...)
move_reweight(trace, proposal, proposal_args, involution; kwargs...)
move_reweight(trace, proposal_fwd, args_fwd, proposal_bwd, args_bwd,
              involution ; kwargs...)

Move-reweight rejuvenation kernel, which takes in a trace and returns a new trace along with a relative importance weight. This can be used for rejuvenation within a particle filter, as described in [1].

Several variants of move_reweight exist, differing in the complexity involved in proposing and re-weighting random choices:

  1. The selection variant regenerates the addresses specified by selection using the model's default proposal.
  2. A proposal generative function and arguments can be provided, to propose new random choices using a custom proposal distribution. proposal must take the original trace as its first input argument.
  3. An involution can also be provided, to handle more complex proposal distributions which add/remove trace addresses.
  4. Separate forward and backward proposal distributions, proposal_fwd and proposal_bwd, can be provided, as long they share the same support. This adjusts the computation of the relative importance weight by scoring the backward choices under the backward proposal.

Similar to metropolis_hastings, a check flag and observations choicemap can be provided as keyword arguments to ensure that observed choices are preserved in the new trace.

[1] R. A. G. Marques and G. Storvik, "Particle move-reweighting strategies for online inference," Preprint series. Statistical Research Report, 2013.

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Care must be taken in choosing forward and backward kernels to reduce variance in the weight updates. A helpful rule-of-thumb when specifying backward kernels is to try and make them locally optimal: If $\pi(x)$ is the initial distribution of particles prior to the rejuvenation move, and $K(x'; x)$ is the forward kernel that will be applied to perturb each particle, then the backward kernel $L(x; x')$ should be designed to approximate the local posterior $P(x | x') \propto \pi(x) K(x'; x)$.