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error : false ---- - -# Using External Samplers - -`Turing` provides several wrapped samplers from external sampling libraries, e.g., HMC samplers from `AdvancedHMC`. -These wrappers allow new users to seamlessly sample statistical models without leaving `Turing` -However, these wrappers might only sometimes be complete, missing some functionality from the wrapped sampling library. -Moreover, users might want to use samplers currently not wrapped within `Turing`. - -For these reasons, `Turing` also makes running external samplers on Turing models easy without any necessary modifications or wrapping! -Throughout, we will use a 10-dimensional Neal's funnel as a running example:: - -```julia -# Import libraries. -using Turing, Random, LinearAlgebra - -d = 10 -@model function funnel() - θ ~ Truncated(Normal(0, 3), -3, 3) - z ~ MvNormal(zeros(d - 1), exp(θ) * I) - return x ~ MvNormal(z, I) -end -``` - -Now we sample the model to generate some observations, which we can then condition on. - -```julia -(; x) = rand(funnel() | (θ=0,)) -model = funnel() | (; x); -``` - -Users can use any sampler algorithm to sample this model if it follows the `AbstractMCMC` API. -Before discussing how this is done in practice, giving a high-level description of the process is interesting. -Imagine that we created an instance of an external sampler that we will call `spl` such that `typeof(spl)<:AbstractMCMC.AbstractSampler`. -In order to avoid type ambiguity within Turing, at the moment it is necessary to declare `spl` as an external sampler to Turing `espl = externalsampler(spl)`, where `externalsampler(s::AbstractMCMC.AbstractSampler)` is a Turing function that types our external sampler adequately. - -An excellent point to start to show how this is done in practice is by looking at the sampling library `AdvancedMH` ((`AdvancedMH`'s GitHub)[[https://github.com/TuringLang/AdvancedMH.jl]) for Metropolis-Hastings (MH) methods. -Let's say we want to use a random walk Metropolis-Hastings sampler without specifying the proposal distributions. -The code below constructs an MH sampler using a multivariate Gaussian distribution with zero mean and unit variance in `d` dimensions as a random walk proposal. - -```julia -# Importing the sampling library -using AdvancedMH -rwmh = AdvancedMH.RWMH(d) -``` - -Sampling is then as easy as: - -```julia -chain = sample(model, externalsampler(rwmh), 10_000) -``` - -## Going beyond the Turing API - -As previously mentioned, the Turing wrappers can often limit the capabilities of the sampling libraries they wrap. -`AdvancedHMC`[^1] ((`AdvancedHMC`'s GitHub)[https://github.com/TuringLang/AdvancedHMC.jl]) is a clear example of this. A common practice when performing HMC is to provide an initial guess for the mass matrix. -However, the native HMC sampler within Turing only allows the user to specify the type of the mass matrix despite the two options being possible within `AdvancedHMC`. -Thankfully, we can use Turing's support for external samplers to define an HMC sampler with a custom mass matrix in `AdvancedHMC` and then use it to sample our Turing model. - -We will use the library `Pathfinder`[^2] ((`Pathfinder`'s GitHub)[https://github.com/mlcolab/Pathfinder.jl]) to construct our estimate of mass matrix. -`Pathfinder` is a variational inference algorithm that first finds the maximum a posteriori (MAP) estimate of a target posterior distribution and then uses the trace of the optimization to construct a sequence of multivariate normal approximations to the target distribution. -In this process, `Pathfinder` computes an estimate of the mass matrix the user can access. - -The code below shows this can be done in practice. - -```julia -using AdvancedHMC, Pathfinder -# Running pathfinder -draws = 1_000 -result_multi = multipathfinder(model, draws; nruns=8) - -# Estimating the metric -inv_metric = result_multi.pathfinder_results[1].fit_distribution.Σ -metric = DenseEuclideanMetric(Matrix(inv_metric)) - -# Creating an AdvancedHMC NUTS sampler with the custom metric. -n_adapts = 1000 # Number of adaptation steps -tap = 0.9 # Large target acceptance probability to deal with the funnel structure of the posterior -nuts = AdvancedHMC.NUTS(tap; metric=metric) - -# Sample -chain = sample(model, externalsampler(nuts), 10_000; n_adapts=1_000) -``` - -## Using new inference methods - -So far we have used Turing's support for external samplers to go beyond the capabilities of the wrappers. -We want to use this support to employ a sampler not supported within Turing's ecosystem yet. -We will use the recently developed Micro-Cannoncial Hamiltonian Monte Carlo (MCHMC) sampler to showcase this. -MCHMC[^3,^4] ((MCHMC's GitHub)[https://github.com/JaimeRZP/MicroCanonicalHMC.jl]) is HMC sampler that uses one single Hamiltonian energy level to explore the whole parameter space. -This is achieved by simulating the dynamics of a microcanonical Hamiltonian with an additional noise term to ensure ergodicity. - -Using this as well as other inference methods outside the Turing ecosystem is as simple as executing the code shown below: - -```julia -using MicroCanonicalHMC -# Create MCHMC sampler -n_adapts = 1_000 # adaptation steps -tev = 0.01 # target energy variance -mchmc = MCHMC(n_adapts, tev; adaptive=true) - -# Sample -chain = sample(model, externalsampler(mchmc), 10_000) -``` - -The only requirement to work with `externalsampler` is that the provided `sampler` must implement the AbstractMCMC.jl-interface [INSERT LINK] for a `model` of type `AbstractMCMC.LogDensityModel` [INSERT LINK]. - -As previously stated, in order to use external sampling libraries within `Turing` they must follow the `AbstractMCMC` API. -In this section, we will briefly dwell on what this entails. -First and foremost, the sampler should be a subtype of `AbstractMCMC.AbstractSampler`. -Second, the stepping function of the MCMC algorithm must be made defined using `AbstractMCMC.step` and follow the structure below: - -``` -# First step -function AbstractMCMC.step{T<:AbstractMCMC.AbstractSampler}( - rng::Random.AbstractRNG, - model::AbstractMCMC.LogDensityModel, - spl::T; - kwargs..., -) - [...] - return transition, sample -end - -# N+1 step -function AbstractMCMC.step{T<:AbstractMCMC.AbstractSampler}( - rng::Random.AbstractRNG, - model::AbstractMCMC.LogDensityModel, - sampler::T, - state; - kwargs..., -) - [...] - return transition, sample -end -``` - -There are several characteristics to note in these functions: - - - There must be two `step` functions: - - + A function that performs the first step and initializes the sampler. - + A function that performs the following steps and takes an extra input, `state`, which carries the initialization information. - - - The functions must follow the displayed signatures. - - The output of the functions must be a transition, the current state of the sampler, and a sample, what is saved to the MCMC chain. - -The last requirement is that the transition must be structured with a field `θ` which contains the values of the parameters of the model for said transition. -This allows `Turing` to seamlessly extract the parameter values at each step of the chain when bundling the chains. -Note that if the external sampler produces transitions that Turing cannot parse the bundling of the samples will be different or fail. - -For practical examples of how to adapt a sampling library to the `AbstractMCMC` interface, the readers can consult the following libraries: - - - (AdvancedMH)[https://github.com/TuringLang/AdvancedMH.jl/blob/458a602ac32a8514a117d4c671396a9ba8acbdab/src/mh-core.jl#L73-L115] - - (AdvancedHMC)[https://github.com/TuringLang/AdvancedHMC.jl/blob/762e55f894d142495a41a6eba0eed9201da0a600/src/abstractmcmc.jl#L102-L170] - - (MicroCanonicalHMC)[https://github.com/JaimeRZP/MicroCanonicalHMC.jl/blob/master/src/abstractmcmc.jl] within `MicroCanonicalHMC`. - -# Refences - -[^1]: Xu et al, (AdvancedHMC.jl: A robust, modular and efficient implementation of advanced HMC algorithms)[http://proceedings.mlr.press/v118/xu20a/xu20a.pdf], 2019 -[^2]: Zhang et al, (Pathfinder: Parallel quasi-Newton variational inference)[https://arxiv.org/abs/2108.03782], 2021 -[^3]: Robnik et al, (Microcanonical Hamiltonian Monte Carlo)[https://arxiv.org/abs/2212.08549], 2022 -[^4]: Robnik and Seljak, (Langevine Hamiltonian Monte Carlo)[https://arxiv.org/abs/2303.18221], 2023