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