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SSMProblems

API

SSMProblems.isdone — Function
isdone(step, particle[, cache])

Determine whether we have reached the last time step of the Markov process. Return true if yes, otherwise return false.

source
SSMProblems.transition!! — Function
transition!!(rng, step, particle[, cache])

Simulate the particle for the next time step from the forward dynamics.

source
+Home · SSMProblems
Edit on GitHub

SSMProblems

Installation

In the julia REPL:

]add SSMProblems

Documentation

SSMProblems defines a generic interface for State Space Problems (SSM). The main objective is to provide a consistent interface to work with SSMs and their logdensities.

Consider a markovian model from[Murray]: state space model

The model is fully specified by the following densities:

  • Initialisation: $f_0(x)$
  • Transition: $f(x)$
  • Emission: $g(x)$

And the dynamics of the model reduces to:

\[\begin{aligned} +x_t | x_{t-1} &\sim f(x_t | x_{t-1}) \\ +y_t | x_t &\sim g(y_t | x_{t}) +\end{aligned}\]

assuming $x_0 \sim f_0(x)$.

The joint law follows:

\[p(x_{0:T}, y_{0:T}) = f_0(x_0) \prod_t g(y_t | x_t) f(x_t | x_{t-1})\]

Users can define their SSM with SSMProblems in the following way:

struct Model <: AbstractStateSpaceModel end
+
+# Define the structure of the latent space
+particleof(::Model) = Float64
+dimension(::Model) = 2
+
+function transition!!(
+    rng::Random.AbstractRNG, 
+    step, 
+    model::Model, 
+    particle::AbstractParticl{<:AbstractStateSpaceModel}
+) 
+    if step == 1
+        ... # Sample from the initial density
+    end
+    ... # Sample from the transition density
+end
+
+function emission_logdensity(step, model::Model, particle::AbstractParticle) 
+    ... # Return log density of the model at *time* `step`
+end
+
+isdone(step, model::Model, particle::AbstractParticle) = ... # Stops the state machine
+
+# Optionally, if the transition density is known, the model can also specify it
+function transition_logdensity(step, prev_particle::AbstractParticle, next_particle::AbstractParticle)
+    ... # Scores the forward transition at `x`
+end

Package users can then consume the model logdensity through calls to emission_logdensity.

For example, a bootstrap filter targeting the filtering distribution $p(x_t | y_{0:t})$ using N particles would roughly follow:

struct Particle{T<:AbstractStateSpaceModel} <: AbstractParticle{T} end 
+
+while !all(map(particle -> isdone(t, model, particles), particles)):
+    ancestors = resample(rng, logweigths)
+    particles = particles[ancestors]
+    for i in 1:N
+        particles[i] = transition!!(rng, t, model, particles[i])
+        logweights[i] += emission_logdensity(t, model, particles[i])
+    end
+end

Interface

SSMProblems.emission_logdensity — Function
emission_logdensity(model, state, observation[, timestep, cache])

Compute the log potential of the current particle. This effectively "reweight" each particle.

source
SSMProblems.transition!! — Function
transition!!(rng, model[, state, timestep, cache])

Simulate the particle for the next time step from the forward dynamics.

source
SSMProblems.transition_logdensity — Function
transition_logdensity(model, prev_state, current_state[, timestep, cache])

(Optional) Computes the log-density of the forward transition if the density is available.

source
  • Murray

    Murray, Lawrence & Lee, Anthony & Jacob, Pierre. (2013). Rethinking resampling in the particle filter on graphics processing units.

diff --git a/dev/search/index.html b/dev/search/index.html index a4e5d81..ec5d170 100644 --- a/dev/search/index.html +++ b/dev/search/index.html @@ -1,2 +1,2 @@ -Search · SSMProblems

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    +Search · SSMProblems

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      diff --git a/dev/search_index.js b/dev/search_index.js index e2e3048..16eb5ab 100644 --- a/dev/search_index.js +++ b/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"#SSMProblems","page":"Home","title":"SSMProblems","text":"","category":"section"},{"location":"#API","page":"Home","title":"API","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Modules = [SSMProblems]\nOrder = [:type, :function]","category":"page"},{"location":"#SSMProblems.AbstractParticle","page":"Home","title":"SSMProblems.AbstractParticle","text":"\n\n\n\n","category":"type"},{"location":"#SSMProblems.emission_logdensity","page":"Home","title":"SSMProblems.emission_logdensity","text":"emission_logdensity(step, particle[, cache])\n\nCompute the log potential of current particle. 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","category":"page"},{"location":"","page":"Home","title":"Home","text":"The model is fully specified by the following densities:","category":"page"},{"location":"","page":"Home","title":"Home","text":"Initialisation: f_0(x)\nTransition: f(x)\nEmission: g(x)","category":"page"},{"location":"","page":"Home","title":"Home","text":"And the dynamics of the model reduces to:","category":"page"},{"location":"","page":"Home","title":"Home","text":"beginaligned\nx_t x_t-1 sim f(x_t x_t-1) \ny_t x_t sim g(y_t x_t)\nendaligned","category":"page"},{"location":"","page":"Home","title":"Home","text":"assuming x_0 sim f_0(x). ","category":"page"},{"location":"","page":"Home","title":"Home","text":"The joint law follows:","category":"page"},{"location":"","page":"Home","title":"Home","text":"p(x_0T y_0T) = f_0(x_0) prod_t g(y_t x_t) f(x_t x_t-1)","category":"page"},{"location":"","page":"Home","title":"Home","text":"Users can define their SSM with SSMProblems in the following way:","category":"page"},{"location":"","page":"Home","title":"Home","text":"struct Model <: AbstractStateSpaceModel end\n\n# Define the structure of the latent space\nparticleof(::Model) = Float64\ndimension(::Model) = 2\n\nfunction transition!!(\n rng::Random.AbstractRNG, \n step, \n model::Model, \n particle::AbstractParticl{<:AbstractStateSpaceModel}\n) \n if step == 1\n ... # Sample from the initial density\n end\n ... # Sample from the transition density\nend\n\nfunction emission_logdensity(step, model::Model, particle::AbstractParticle) \n ... # Return log density of the model at *time* `step`\nend\n\nisdone(step, model::Model, particle::AbstractParticle) = ... # Stops the state machine\n\n# Optionally, if the transition density is known, the model can also specify it\nfunction transition_logdensity(step, prev_particle::AbstractParticle, next_particle::AbstractParticle)\n ... # Scores the forward transition at `x`\nend","category":"page"},{"location":"","page":"Home","title":"Home","text":"Package users can then consume the model logdensity through calls to emission_logdensity. ","category":"page"},{"location":"","page":"Home","title":"Home","text":"For example, a bootstrap filter targeting the filtering distribution p(x_t y_0t) using N particles would roughly follow:","category":"page"},{"location":"","page":"Home","title":"Home","text":"struct Particle{T<:AbstractStateSpaceModel} <: AbstractParticle{T} end \n\nwhile !all(map(particle -> isdone(t, model, particles), particles)):\n ancestors = resample(rng, logweigths)\n particles = particles[ancestors]\n for i in 1:N\n particles[i] = transition!!(rng, t, model, particles[i])\n logweights[i] += emission_logdensity(t, model, particles[i])\n end\nend","category":"page"},{"location":"#Interface","page":"Home","title":"Interface","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Modules = [SSMProblems]\nOrder = [:type, :function]","category":"page"},{"location":"#SSMProblems.AbstractStateSpaceModel","page":"Home","title":"SSMProblems.AbstractStateSpaceModel","text":"AbstractStateSpaceModel\n\n\n\n\n\n","category":"type"},{"location":"#SSMProblems.emission_logdensity","page":"Home","title":"SSMProblems.emission_logdensity","text":"emission_logdensity(model, state, observation[, timestep, cache])\n\nCompute the log potential of the current particle. 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