From 998cdf5ffcb8a70474a8fd310d8b3adf046e34e3 Mon Sep 17 00:00:00 2001 From: jaimerz Date: Thu, 19 Oct 2023 17:35:20 +0100 Subject: [PATCH] folder name conv --- .../Manifest.toml | 1466 +++++++++++++++++ .../Project.toml | 8 + .../external-samplers.jmd | 169 ++ 3 files changed, 1643 insertions(+) create mode 100644 tutorials/docs-16-using-turing-external-samplers/Manifest.toml create mode 100644 tutorials/docs-16-using-turing-external-samplers/Project.toml create mode 100644 tutorials/docs-16-using-turing-external-samplers/external-samplers.jmd diff --git a/tutorials/docs-16-using-turing-external-samplers/Manifest.toml b/tutorials/docs-16-using-turing-external-samplers/Manifest.toml new file mode 100644 index 000000000..6a0fc46ca --- /dev/null +++ b/tutorials/docs-16-using-turing-external-samplers/Manifest.toml @@ -0,0 +1,1466 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.9.3" +manifest_format = "2.0" +project_hash = 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/dev/null +++ b/tutorials/docs-16-using-turing-external-samplers/external-samplers.jmd @@ -0,0 +1,169 @@ +--- +title: Using External Sampler +permalink: /tutorials/:name/ +mathjax: true +weave_options: + 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