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Quick and dirty example of a mixture sampler using some internals of MCMCTempering.jl.
# This file is machine-generated - editing it directly is not advised
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using Distributions, LinearAlgebra, AdvancedMH, AdvancedHMC, AbstractMCMC, MCMCTempering, ForwardDiff
using Setfield: Setfield
using LogDensityProblems: LogDensityProblems
using Random: Random
# Source: https://turinglang.org/MCMCTempering.jl/dev/getting-started/
# Make `AdvancedMH` compatible with `MCMCTempering`.
MCMCTempering.getparams_and_logprob(transition::AdvancedMH.Transition) = transition.params, transition.lp
function MCMCTempering.setparams_and_logprob!!(transition::AdvancedMH.Transition, params, lp)
return AdvancedMH.Transition(params, lp)
end
# Make `AdvancedHMC` compatible with `MCMCTempering`.
# Provides a convenient way of "mutating" (read: reconstructing) types with different values
# for specified fields; see usage below.
function MCMCTempering.getparams_and_logprob(state::AdvancedHMC.HMCState)
t = state.transition
return t.z.θ, t.z.ℓπ.value
end
function MCMCTempering.setparams_and_logprob!!(model, state::AdvancedHMC.HMCState, params, logprob)
# NOTE: Need to recompute the gradient because it might be used in the next integration step.
hamiltonian = AdvancedHMC.Hamiltonian(state.metric, model)
return Setfield.@set state.transition.z = AdvancedHMC.phasepoint(
hamiltonian, params, state.transition.z.r;
ℓκ=state.transition.z.ℓκ
)
end
# For post-processing.
function MCMCTempering.getparams_and_logprob(t::AdvancedHMC.Transition)
return t.z.θ, t.z.ℓπ.value
end
# Implement a `MixtureSampler`.
struct MixtureSampler{S,Ws} <: AbstractMCMC.AbstractSampler
samplers::S
weights::Ws
end
struct MixtureState{Ss,S}
states::Ss
current::S
end
# Initial step.
function AbstractMCMC.step(
rng::Random.AbstractRNG,
model::AbstractMCMC.LogDensityModel,
sampler::MixtureSampler;
kwargs...
)
transition_and_state_initials = map(sampler.samplers) do s
AbstractMCMC.step(rng, model, s; kwargs...)
end
# Sample a transition using the weights.
idx = rand(rng, Categorical(sampler.weights))
state_initial = MixtureState(map(last, transition_and_state_initials), last(transition_and_state_initials[idx]))
transition_initial = first(transition_and_state_initials[idx])
return transition_initial, state_initial
end
# Subsequent iterations.
function AbstractMCMC.step(
rng::Random.AbstractRNG,
model::AbstractMCMC.LogDensityModel,
sampler::MixtureSampler,
state::MixtureState;
kwargs...
)
# Sample the sampler using the weights.
idx = rand(rng, Categorical(sampler.weights))
sampler_inner = sampler.samplers[idx]
# Update the state we're going to use from the current state.
state_inner = state.states[idx]
state_inner_updated = if state_inner === state.current
state_inner
else
# Updates `state_inner` using `state.current`.
MCMCTempering.state_from(model, state_inner, state.current)
end
# Step the inner sampler.
transition_inner, state_inner_current = AbstractMCMC.step(rng, model, sampler_inner, state_inner_updated; kwargs...)
state_new = Setfield.@set(state.states[idx] = state_inner_current)
return transition_inner, Setfield.@set(state_new.current = state_inner_current)
end
using LinearAlgebra
using Turing
# Include the implementation of `MixtureSampler` and the necessary sampling methods.
include("mixture-sampler-shared.jl")
# Model.
@model function demo()
x ~ MixtureModel(
MvNormal,
[([-10], I), ([10], I)], # parameters
[0.5, 0.5] # weights
)
end
# HACK: This is a temporary workaround for the fact that `MixtureModel` doesn't have a `bijector` method.
function Bijectors.bijector(d::MixtureModel)
# Only okay to do if all the components have the same bijector.
b = bijector(first(components(d)))
if any(!=(b) ∘ bijector, components(d))
throw(ArgumentError("All components must have the same bijector."))
end
return b
end
# Instantiate the model.
model = demo()
# Convert into a `LogDensityFunction` so we can pass directly to AdvancedHMC.jl, etc.
target_model = DynamicPPL.LogDensityFunction(model);
# Link because we need to work in unconstrained space.
# For this particular model, it's not actually necessary, but in general it is.
# NOTE: This will cause the resulting parameters to be in unconstrained space, not the original space.
# But we can easily map this back after sampling.
DynamicPPL.link!!(target_model.varinfo, target_model.model);
# Now we're ready to sample.
num_iterations = 10_000
num_adapts = 1000
num_chains = 4
# First we run a few preliminary chains with HMC so we can determine relevant modes.
num_preliminary_iterations = 1000 # use fewer iterations for preliminary chains
sampler_preliminary = AdvancedHMC.NUTS(0.8)
chains_preliminary = sample(
target_model,
sampler_preliminary,
MCMCSerial(),
num_preliminary_iterations,
num_chains;
n_adapts=num_adapts
);
# Use means and variances of the chains to construct a proposal distribution.
means = map(chains_preliminary) do chain
mean(MCMCTempering.getparams, chain)
end
variances = map(chains_preliminary) do chain
var(map(MCMCTempering.getparams, chain))
end
proposal_components = map(means, variances) do μ, σ²
MvNormal(μ, Diagonal(σ²))
end
# Mixture proposal of the HMC chains.
proposal = MixtureModel(proposal_components)
# Construct MH sampler which uses our specified proposal distribution.
proposal_mh = StaticProposal(proposal);
sampler_mh = MetropolisHastings(proposal_mh);
# Construct HMC sampler which we'll use for the "local" exploration.
sampler_hmc = AdvancedHMC.NUTS(0.8);
# Mixture sampler.
proposal_portion = 0.1 # this parameter might need some tweaking depending on the problem
sampler = MixtureSampler([sampler_mh, sampler_hmc], [proposal_portion, 1 - proposal_portion]);
# Sample.
chains = sample(
target_model,
sampler,
MCMCSerial(),
num_iterations,
num_chains;
4;
n_adapts=num_adapts,
);
chain = reduce(vcat, chains);
mean(first ∘ MCMCTempering.getparams, chain)
using StatsPlots
plot(map(first ∘ MCMCTempering.getparams, chain), label="")
density(map(first ∘ MCMCTempering.getparams, chain), label="")
# Include the implementation of `MixtureSampler` and the necessary sampling methods.
include("mixture-sampler-shared.jl")
# Define the target distribution.
target_distribution = MixtureModel(
MvNormal,
[([-10], I), ([10], I)], # parameters
[0.5, 0.5] # weights
);
# Implement LogDensityProblems.jl-interface for `Distribution`.
struct DistributionLogDensity{D<:Distribution}
d::D
end
LogDensityProblems.logdensity(d::DistributionLogDensity, x) = loglikelihood(d.d, x)
LogDensityProblems.dimension(d::DistributionLogDensity) = length(d.d)
LogDensityProblems.capabilities(::Type{<:DistributionLogDensity}) = LogDensityProblems.LogDensityOrder{0}()
# Wrap our target distribution.
target_model = DistributionLogDensity(target_distribution);
# Now we can sample!
# MH sampler.
proposal_mh = StaticProposal(target_distribution); # we're cheating
sampler_mh = MetropolisHastings(proposal_mh);
# HMC sampler.
sampler_hmc = AdvancedHMC.HMC(1e-2, 32);
# Mixture sampler.
sampler = MixtureSampler([sampler_mh, sampler_hmc], [0.1, 0.9]);
# Sample.
chain = sample(target_model, sampler, 1000; n_adapts=0);
mean(first ∘ MCMCTempering.getparams, chain)
using StatsPlots
plot(map(first ∘ MCMCTempering.getparams, chain), label="")
[deps]
AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
AdvancedHMC = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
AdvancedMH = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
LogDensityProblems = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
LogDensityProblemsAD = "996a588d-648d-4e1f-a8f0-a84b347e47b1"
MCMCTempering = "ce233488-44ea-4441-b732-192676ce2298"
Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
@torfjelde
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