ThermodynamicIntegration

Thermodynamic Integration

Thermodynamic integration is a technique from physics to get an accurate estimate of the log evidence. By creating a schedule going from the prior to the posterior and estimating the log likelihood at each step one gets a stable ad robust estimate of the log evidence.

A simple example

A simple package to compute Thermodynamic Integration for computing the evidence in a Bayesian setting. You need to provide the logprior and the loglikelihood as well as an initial sample:

    using Distributions, ThermodynamicIntegration
    D = 5
    prior = MvNormal(0.5 * ones(D)) # The prior distribution
    likelihood = MvNormal(2.0 * ones(D))
    logprior(x) = logpdf(prior, x) # The log-prior function
    loglikelihood(x) = logpdf(likelihood, x) # The log-likelihood function

    alg = ThermInt(n_samples=5000) # We are going to sample 5000 samples at every step

    logZ = alg(logprior, loglikelihood, rand(prior)) # Compute the log evidence
    # -8.244829688529377
    true_logZ = -0.5 * (logdet(cov(prior) + cov(likelihood)) + D * log(2π)) # we compare twith the true value
    # -8.211990123364176

You can also simply pass a Turing model :

    using Turing
    @model function gauss(y)
        x ~ prior
        y ~ MvNormal(x, cov(likelihood))
    end

    alg = ThermInt(n_samples=5000)
    model = gauss(zeros(D))
    turing_logZ = alg(model)
    # # -8.211990123364176

Parallel sampling

The algorithm also works on multiple threads by calling :

    alg = ThermInt(n_samples=5000) 
    logZ = alg(logprior, loglikelihood, rand(prior), TIParallelThreads())

Sampling methods

Right now sampling is based on AdvancedHMC.jl, with the ForwardDiff AD backend. To change the backend to Zygote or ReverseDiff (recommended for variables with large dimensions you can do:

    using Zygote # (or ReverseDiff)
    ThermoDynamicIntegration.set_adbackend(:Zygote) # (or :ReverseDiff)

More samplers will be available in the future.

Further options

You can disactivate the progress by calling progress=false

    alg()

Red-Portal / ThermodynamicIntegration.jl