SSMProblems.jl

A minimalist framework to define state space models (SSMs) and their associated log-densities to feed into inference algorithms.

Basic interface

This package defines the basic interface needed to run inference on state space as the following:

# Wrapper for model dynamics and observation process
abstract type LatentDynamics end
abstract type ObservationDynamics end

# Define the initialisation/transition distribution for the latent dynamics
function distribution(dyn::LatentDynamics, ...) end

# Define the observation distribution
function distribution(obs::ObservationProcess, ...) end

# Combine the latent dynamics and observation process to form a SSM
model = StateSpaceModel(dyn, obs)

For specific details on the interface, please refer to the package documentation.

Linear Gaussian State Space Model

As a concrete example, the following snippet of pseudo-code defines a linear Gaussian state space model. Note the inclusion of the extra parameter in each method definition. This is a key feature of the SSMProblems interface which allows for the definition of more complex models in a performant fashion, explained in more details in the package documentation.

using SSMProblems, Distributions

# Model parameters
sig_u, sig_v  = 0.1, 0.2

struct LinearGaussianLatentDynamics <: LatentDynamics end

# Initialisation distribution
function distribution(dyn::LinearGaussianLatentDynamics, extra::Nothing)
    return Normal(0.0, sig_u)
end

# Transition distribution
function distribution(
    dyn::LinearGaussianLatentDynamics,
    step::Int,
    state::Float64,
    extra::Nothing
)
    return Normal(state, sig_u)
end

struct LinearGaussianObservationProcess <: ObservationProcess end

# Observation distribution
function distribution(
    obs::LinearGaussianObservationProcess,
    step::Int,
    state::Float64,
    extra::Nothing
)
    return Normal(state, sig_v)
end