BolfiProblem(X, Y; kwargs...)
BolfiProblem(data::ExperimentData; kwargs...)
BolfiProblem(::BossProblem, ::Likelihood, x_prior::MultivariateDistribution)
BolfiProblem(::BossProblem, ::Likelihood, x_prior::MultivariateDistribution, y_sets::Matrix{Bool})

Defines the likelihood-free inference problem and stores all data.

Args

The initial data are provided either as two column-wise matrices X and Y with inputs and outputs of the simulator respectively, or as an instance of BOSS.ExperimentData.

Currently, at least one datapoint has to be provided (purely for implementation reasons).

Kwargs

• f::Any: The simulation to be queried for data.
• bounds::AbstractBounds: The basic box-constraints on x. This field is mandatory.
• discrete::AbstractVector{<:Bool}: Can be used to designate some dimensions of the domain as discrete.
• cons::Union{Nothing, Function}: Used to define arbitrary nonlinear constraints on x. Feasible points x must satisfy all(cons(x) .> 0.). An appropriate acquisition maximizer which can handle nonlinear constraints must be used if cons is provided. (See BOSS.AcquisitionMaximizer.)
• acquisition::BolfiAcquisition: Defines the acquisition function.
• kernel::Kernel: The kernel used in the GP. Defaults to the Matern32Kernel().
• lengthscale_priors::AbstractVector{<:MultivariateDistribution}: The prior distributions for the length scales of the GP. The lengthscale_priors should be a vector of y_dim x_dim-variate distributions where x_dim and y_dim are the dimensions of the input and output of the model respectively.
• amplitude_priors::AbstractVector{<:UnivariateDistribution}: The prior distributions for the amplitude hyperparameters of the GP. The amplitude_priors should be a vector of y_dim univariate distributions.
• noise_std_priors::AbstractVector{<:UnivariateDistribution}: The prior distributions of the standard deviations the Gaussian simulator noise on each dimension of the output y.
• likelihood::Likelihood: The likelihood of the experiment observation y_o.
• x_prior::MultivariateDistribution: The prior p(x) on the input parameters.
• y_sets::Matrix{Bool}: Optional parameter intended for advanced usage. The binary columns define subsets y_1, ..., y_m of the observation dimensions within y. The algorithm then trains multiple posteriors p(θ|y_1), ..., p(θ|y_m) simultaneously. The posteriors can be compared after the run is completed to see which observation subsets are most informative.

Represents the assumed likelihood of the experiment observation $y_o$.

Defining a Custom Likelihood

To define a custom likelihood, create a new struct CustomLike <: Likelihood and implement the following methods;

• loglike(::CustomLike, z::AbstractVector{<:Real}) where z is the simulator output
• approx_likelihood(::CustomLike, bolfi, gp_post): Necessary to be able to use approx_posterior.
• likelihood_mean(::CustomLike, bolfi, gp_post): Necessary to be able to use posterior_mean.
• sq_likelihood_mean(::CustomLike, bolfi, gp_post): Necessary to be able to use posterior_variance.
• get_subset(::CustomLike, y_set::AsbtractVector{<:Bool}): Necessary for BolfiProblems where !isnothing(problem.y_sets).

NormalLikelihood(; y_obs, std_obs)

The observation is assumed to have been generated from a normal distribution as y_o \sim Normal(f(x), Diagonal(std_obs)). We can use the simulator to query z = f(x).

Kwargs

• y_obs::Vector{Float64}: The observed values from the real experiment.
• std_obs::Union{Vector{Float64}, Nothing}: The standard deviations of the Gaussian observation noise on each dimension of the "ground truth" observation. (If the observation is considered to be generated from the simulator and not some "real" experiment, provide std_obs = nothing` and the adaptively trained simulation noise deviation will be used in place of the experiment noise deviation as well. This may be the case for some toy problems or benchmarks.)

LogNormalLikelihood(; y_obs, std_obs)

The observation is assumed to have been generated from a normal distribution as y_o \sim LogNormal(f(x), Diagonal(std_obs)). We can use the simulator to query z = f(x).

In many cases, one may want to take the logarithm of the output of the simulator. Meaning, if one has simulator z = sim(x), one would define f as y = f(x) = log(sim(x)). This way, the y values with high likelihood will have similar values to the z values.

Kwargs

• y_obs::Vector{Float64}: The observed values from the real experiment.
• std_obs::Vector{Float64}: The standard deviations of the LogNormal observation noise. (If the observation is considered to be generated from the simulator and not some "real" experiment, provide std_obs = nothing` and the adaptively trained simulation noise deviation will be used in place of the experiment noise deviation as well. This may be the case for some toy problems or benchmarks.)

BinomialLikelihood(; y_obs, trials, kwargs...)

The observation is assumed to have been generated from a Binomial distribution as y_o \sim Binomial(trials, f(x)). We can use the simulator to query z = f(x).

The simulator should only return values between 0 and 1. The GP estimates are clamped to this range.

Kwargs

• y_obs::Vector{Int64}: The observed values from the real experiment.
• trials::Vector{Int64}: The number of trials for each observation dimension.
• int_grid_size::Int64: The number of samples used to approximate the expected likelihood.

GutmannNormalLikelihood(; std_obs::Vector{Float64})

The observation is assumed to have been generated from a normal distribution as y_o \sim Normal(f(x), Diagonal(std_obs)). We can use the simulator to query z = f(x).

This likelihood follows the equations from Gutmann et al. [1,2].

It is defined in a slightly different way than the other Likelihoods. Namely, this likelihood requires the simulator to return a single non-negative scalar value, describing the discrepancy \delta of the simulator outcome from the real observation.

(See that the real observation y_obs is not provided as a parameter to GutmannNormalLikelihood as in the case of other Likelihoods. Instead, the observation y_obs should be used to calculate the discrepancy \delta in the simulator f provided to BolfiProblem. The simulator should return the discrepancy as a vector [\delta] of length 1.)

The likelihood is then defined as $P[\delta < \epslion]$ instead of $P[\delta = 0]$, which would correspond more closely to the other Likelihoods. The parameter \epsilon is the acceptance threshold.

Kwargs

• ϵ::Float64: The threshold for the discrepancy from the real observation.

References

[1] Gutmann, Michael U., and Jukka Cor. "Bayesian optimization for likelihood-free inference of simulator-based statistical models." Journal of Machine Learning Research 17.125 (2016): 1-47.

[2] Järvenpää, Marko, et al. "Efficient acquisition rules for model-based approximate Bayesian computation." (2019): 595-622.

An abstract type for BOLFI acquisition functions.

Required API for subtypes of BolfiAcquisition:

• Implement method (::CustomAcq)(::Type{<:UniFittedParams}, ::BolfiProblem, ::BolfiOptions) -> (x -> ::Real).

Optional API for subtypes of BolfiAcquisition:

• Implement method (::CustomAcq)(::Type{<:MultiFittedParams}, ::BolfiProblem, ::BolfiOptions) -> (x -> ::Real). A default fallback is provided for MultiFittedParams, which averages individual acquisition functions for each sample.

PostVarAcq()

Selects the new evaluation point by maximizing the variance of the posterior approximation.

MWMVAcq(; kwargs...)

The Mass-Weighted Mean Variance acquisition function.

Selects the next evaluation point by maximizing a weighted average of the variances of the individual posterior approximations given by different sensor sets. The weights are determined as the total probability mass of the current data w.r.t. each approximate posterior.

Keywords

• samples::Int: The number of samples used to estimate the evidence.

An abstract type for BOLFI termination conditions.

Implementing custom termination condition:

• Create struct CustomTermCond <: BolfiTermCond
• Implement method (::CustomTermCond)(::BolfiProblem) -> ::Bool

AEConfidence(; kwargs...)

Calculates the q-confidence region of the expected and the approximate posteriors. Terminates after the IoU of the two confidence regions surpasses r.

Keywords

• max_iters::Union{Nothing, <:Int}: The maximum number of iterations.
• samples::Int: The number of samples used to approximate the confidence regions and their IoU ratio. Only has an effect if isnothing(xs).
• xs::Union{Nothing, <:AbstractMatrix{<:Real}}: Can be used to provide a pre-sampled set of parameter samples from the x_prior defined in BolfiProblem.
• q::Float64: The confidence value of the confidence regions. Defaults to q = 0.95.
• r::Float64: The algorithm terminates once the IoU ratio surpasses r. Defaults to r = 0.95.

UBLBConfidence(; kwargs...)

Calculates the q-confidence region of the UB and LB approximate posterior. Terminates after the IoU of the two confidence intervals surpasses r. The UB and LB confidence intervals are calculated using the GP mean +- n GP stds.

Keywords

• max_iters::Union{Nothing, <:Int}: The maximum number of iterations.
• samples::Int: The number of samples used to approximate the confidence regions and their IoU ratio. Only has an effect if isnothing(xs).
• xs::Union{Nothing, <:AbstractMatrix{<:Real}}: Can be used to provide a pre-sampled set of parameter samples from the x_prior defined in BolfiProblem.
• n::Float64: The number of predictive deviations added/substracted from the GP mean to get the two posterior approximations. Defaults to n = 1..
• q::Float64: The confidence value of the confidence regions. Defaults to q = 0.8.
• r::Float64: The algorithm terminates once the IoU ratio surpasses r. Defaults to r = 0.8.

BolfiOptions(; kwargs...)

Stores miscellaneous settings.

Keywords

• info::Bool: Setting info=false silences the algorithm.
• debug::Bool: Set debug=true to print stactraces of caught optimization errors.
• parallel_evals::Symbol: Possible values: :serial, :parallel, :distributed. Defaults to :parallel. Determines whether to run multiple objective function evaluations within one batch in serial, parallel, or distributed fashion. (Only has an effect if batching AM is used.)
• callback::Union{<:BossCallback, <:BolfiCallback}: If provided, the callback will be called before the BO procedure starts and after every iteration.

If a callback cb of type BolfiCallback is defined in BolfiOptions, the method cb(::BolfiProblem; kwargs...) will be called in every iteration.

cb(problem::BolfiProblem;
    model_fitter::BOSS.ModelFitter,
    acq_maximizer::BOSS.AcquisitionMaximizer,
    acquisition::BOLFI.AcqWrapper,              # `BolfiAcquisition` wrapped into `AcqWrapper`
    term_cond::TermCond,                        # either `BOSS.TermCond` or a `BolfiTermCond` wrapped into `TermCondWrapper`
    options::BossOptions,
    first::Bool,
)