# GenParticleFilters.jl

Building blocks for simple and advanced particle filtering in Gen, a general-purpose probabilistic programming system.

## Installation

Press `]`

at the Julia REPL to enter the package manager, then run:

`add GenParticleFilters`

To install the development version, run:

`add https://github.com/probcomp/GenParticleFilters.jl.git`

## Features

In addition to basic particle filtering functionality (i.e., initializing a particle filter and updating it with new observations), this package provides support for:

- Particle updates that allow discarding of old choices, provided that backward kernels are specified [1]
- Multiple resampling methods, including variance-reducing methods such as residual resampling [2]
- Custom priority weights for resampling, to control the aggressiveness of pruning [3]
- Metropolis-Hasting (i.e. move-accept) rejuvenation moves, to increase particle diversity [4]
- Move-reweight rejuvenation, which increases particle diversity while reweighting particles [5]
- Sequential Monte Carlo over a series of distinct models, via trace translators [6]
- Utility functions to compute distributional statistics (e.g. mean and variance) for the inferred latent variables

## Example

Suppose we are trying to infer the position `y`

of an object that is either staying still or moving sinusoidally, given noisy measurements `y_obs`

. We can write a model of this object's motion as an `@gen`

function:

```
@gen function object_motion(T::Int)
y, moving = 0, false
y_obs_all = Float64[]
for t=1:T
moving = {t => :moving} ~ bernoulli(moving ? 0.75 : 0.25)
vel_y = moving ? sin(t) : 0.0
y = {t => :y} ~ normal(y + vel_y, 0.01)
y_obs = {t => :y_obs} ~ normal(y, 0.25)
push!(y_obs_all, y_obs)
end
return y_obs_all
end
```

We can then construct a particle filter with resampling and rejuvenation moves, in order to infer both the object's position `y`

and whether the object was `moving`

at each timestep.

```
function particle_filter(observations, n_particles, ess_thresh=0.5)
# Initialize particle filter with first observation
n_obs = length(observations)
obs_choices = [choicemap((t => :y_obs, observations[t])) for t=1:n_obs]
state = pf_initialize(object_motion, (1,), obs_choices[1], n_particles)
# Iterate across timesteps
for t=2:n_obs
# Resample and rejuvenate if the effective sample size is too low
if effective_sample_size(state) < ess_thresh * n_particles
# Perform residual resampling, pruning low-weight particles
pf_resample!(state, :residual)
# Perform a rejuvenation move on past choices
rejuv_sel = select(t-1=>:moving, t-1=>:y, t=>:moving, t=>:y)
pf_rejuvenate!(state, mh, (rejuv_sel,))
end
# Update filter state with new observation at timestep t
pf_update!(state, (t,), (UnknownChange(),), obs_choices[t])
end
return state
end
```

We can then run the particle filter on a sequence of observations, e.g., of the object staying still for 5 timesteps then oscillating for 5 timesteps:

```
# Generate synthetic dataset of object motion
constraints = choicemap([(t => :moving, t > 5) for t in 1:10]...)
trace, _ = generate(object_motion, (10,), constraints)
observations = get_retval(trace)
# Run particle filter with 100 particles
state = particle_filter(observations, 100)
```

We can then use `mean`

and `var`

to compute the empirical posterior mean
and variance for variables of interest:

```
julia> mean(state, 5=>:moving) |> x->round(x, digits=2) # Prob. motion at t=5
0.07
julia> var(state, 5=>:moving) |> x->round(x, digits=2) # Variance at t=5
0.07
julia> mean(state, 6=>:moving) |> x->round(x, digits=2) # Prob. motion at t=6
0.95
julia> var(state, 6=>:moving) |> x->round(x, digits=2) # Variance at t=6
0.05
```

We see that the filter accurately infers a change in motion from `t=5`

to `t=6`

.

## References

[1] P. D. Moral, A. Doucet, and A. Jasra, “Sequential Monte Carlo samplers,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 68, no. 3, pp. 411–436, 2006.

[2] R. Douc and O. Cappé, "Comparison of resampling schemes for particle filtering," in ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005., 2005, pp. 64-69.

[3] R. Chen, “Sequential Monte Carlo methods and their applications,” in Markov Chain Monte Carlo, vol. Volume 7, 0 vols., Singapore University Press, 2005, pp. 147–182.

[4] N. Chopin, “A sequential particle filter method for static models,” Biometrika 89.3, 2000, pp. 539-552.

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

[6] M. Cusumano-Towner, B. Bichsel, T. Gehr, M. Vechev, and V. K. Mansinghka, “Incremental inference for probabilistic programs,” in Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation, Philadelphia PA USA, Jun. 2018, pp. 571–585.