GMatrix( d::Int64 )




compute transformation matrix G.
#Arguments
- `d::Int64`:        number of hypothesis used for prediction.
#Return
- `Matrix{Float64}`: transformation matrix G.

bootstrapPosteriorCorEstimation( predictions::Matrix{Float64}, t::Vector{Float64}, samplingBatchSize::Int64, nrRuns::Int64 )




compute posterior p( h* = h | S ).
#Arguments
- `predictions::Matrix{Float64}`: each column is the prediction of one hypothesis.
- `t::Vector{Float64}`:           label vector.
- `samplingBatchSize::Int64`:     sample size per main iteration.
- `nrRuns::Int64`:                number of main  iterations.
#Return
- `Vector{Float64}`:              posterior p( h* = h | S ).

bootstrapPosteriorCorEstimation( predictions::Vector{Matrix{Float64}}, T::Matrix{Float64}, samplingFactor::Float64, nrRuns::Int64 )




compute posterior p( h* = h | S ).
#Arguments
- `predictions::Matrix{Float64}`: each column is the prediction of one hypothesis.
- `T::Matrix{Float64}`:           label matrix.
- `samplingBatchSize::Int64`:     sample size per main iteration.
- `nrRuns::Int64`:                number of main  iterations.
#Return
- `Vector{Float64}`:              posterior p( h* = h | S ).

bootstrapPosteriorEstimation!( errMat::Matrix{Float64}, samplingBatchSize::Int64, nrRuns::Int64, p::Array{Float64} )



compute posterior p( h* = h | S ).
#Arguments
- `errMat::Matrix{Float64}}`: each column is the prediction error of one hypothesis.
- `samplingBatchSize::Int64`: sample size per main iteration.
- `nrRuns::Int64`:            number of passes over predictions.
- `p::Vector{Float64}`:       resulting posterior p( h* = h | S ).
#Return
- `nothing`:                  nothing.

bootstrapPosteriorEstimation( errMat::Matrix{Float64}, samplingBatchSize::Int64, nrRuns::Int64 )




compute posterior p( h* = h | S ).
#Arguments
- `errMat::Matrix{Float64}}`: each column is the prediction error of one hypothesis.
- `samplingBatchSize::Int64`: sample size per main iteration.
- `nrRuns::Int64`:            number of passes over predictions.
#Return
- `Vector{Float64}`:          Distribution p( h* = h | S ).

directOptimHinge( predMat::Matrix{Float64}, t::Vector{Float64}, p::Vector{Float64} )




compute refined solution _for_ mixing parameter p.
#Arguments
- `predMat::Matrix{Float64}`: each column is the prediction _of_ one hypothesis.
- `t::Vector{Float64}`:       label vector.
- `p::Vector{Float64}`:       initial solution for mixing coefficients.
#Return
- `Vector{Float64}`:          improved initial solution.

directOptimNaiveMSE( predMat::Matrix{Float64}, t::Vector{Float64}, p::Vector{Float64} )




compute refined solution _for_ mixing parameter p.
#Arguments
- `predMat::Matrix{Float64}`: each column is the prediction _of_ one hypothesis.
- `t::Vector{Float64}`:       label vector.
- `p::Vector{Float64}`:       initial solution for mixing coefficients.
#Return
- `Vector{Float64}`:          improved initial solution.

dirichletPosteriorEstimation!( errMat::Matrix{Float64}, nrRuns::Int64, α_::Float64, p::Vector{Float64} )




compute posterior p( h* = h | S ).
#Arguments
- `errMat::Matrix{Float64}`: each column is the prediction error of one hypothesis.
- `nrRuns::Int64`:           number of passes over predictions.
- `α_::Float64`:             meta parameter value.
- `p::Vector{Float64}`:      return value posterior p( h* = h | S ).
#Return
- `nothing`:                 nothing.

dirichletPosteriorEstimation( errMat::Matrix{Float64}, nrRuns::Int64, α_::Float64 )




compute posterior p( h* = h | S ).
#Arguments
- `errMat::Matrix{Float64}`: each column is the prediction error of one hypothesis.
- `nrRuns::Int64`:           number of main  iterations.
- `α_::Float64`:             scalar prior parameter.
#Return
- `Vector{Float64}`:         posterior p( h* = h | S ).

dirichletPosteriorEstimation( errMat::Matrix{Float64}, G::Matrix{Float64}, nrRuns::Int64, α_::Float64 )




compute posterior p( h* = h | S ).
# Arguments
- `errMat::Matrix{Float64}`: each column is the prediction error of one hypothesis.
- `G::Matrix{Float64}`:      transformation matrix G.
- `nrRuns::Int64`:           number of sampling runs.
- `α_::Float64`:             scalar prior parameter.
- `sampleSize::Int64`:       number of samples per run.
# Return
- `Vector{Float64}`:         posterior distribution

dirichletPosteriorEstimationV2( errMat::Matrix{Float64}, nrRuns::Int64, α_::Float64, sampleSize::Int64 )




compute posterior p( h* = h | S ), alternative version for improved performance.
# Arguments
- `errMat::Matrix{Float64}`: each column is the prediction of one hypothesis.
- `nrRuns::Int64`:           number of sampling runs.
- `α_::Float64`:             scalar prior parameter.
- `sampleSize::Int64`:       number of samples per run.
# Return
- `Vector{Float64}`:         posterior distribution p( h* = h | S ).

dirichletPosteriorEstimationV2( errMat::Matrix{Float64}, G::Matrix{Float64}, nrRuns::Int64, α_::Float64, sampleSize::Int64 )




compute posterior p( h* = h | S ), alternative version for improved performance.
# Arguments
- `errMat::Matrix{Float64}`: each column is the prediction error of one hypothesis.
- `G::Matrix{Float64}`:      transformation matrix G.
- `nrRuns::Int64`:           number of sampling runs.
- `α_::Float64`:             scalar prior parameter.
- `sampleSize::Int64`:       number of samples per run.
# Return
- `Vector{Float64}`:         posterior distribution posterior p( h* = h | S ).

metaParamSearchValidationDirichlet( Y::Matrix{Float64}, t::Vector{Float64}, nrRuns::Int64, minVal::Float64, maxVal::Float64, nSteps::Int64, holdout::Float64, lossFunc )    




compute best α parameter regarding predictive performance.
#Arguments
- `Y::Matrix{Float64}`: each column is the prediction error of one hypothesis.
- `t::Vector{Float64}`: label vector.
- `nrRuns::Int64`:      number of passes over predictions.
- `minVal::Float64`:    minimum value of α.
- `maxVal::Float64`:    maximum value of α.
- `nSteps::Int64`:      number of steps between min and max val.
- `holdout::Float64`:   percentage used in holdout.
- `lossFunc`:           error function handle.
#Return
- `Vector{Float64} x2`: α_sequence, performance_sequence.

objFunctionHinge( p::Vector{Float64}; predMat::Matrix{Float64}, t::Vector{Float64} )




evaluate MeanSquaredError under given params.
#Arguments
- `p::Vector{Float64}`:       initial solution.
- `predMat::Matrix{Float64}`: each column represents predictions of one model.
- `t::Vector{Float64}`:       ground truth labels.
#Return
- `Float64`:                  hingeLoss.

objFunctionMSE( p::Vector{Float64}; predMat::Matrix{Float64}, t::Vector{Float64} )




evaluate MeanSquaredError under given params.
#Arguments
- `p::Vector{Float64}`:       initial solution.
- `predMat::Matrix{Float64}`: each column represents predictions of one model.
- `t::Vector{Float64}`:       ground truth labels.
#Return
- `Float64`:                  MeanSquaredError.

predictEnsemble( predictions::Matrix{Float64}, weights::Vector{Float64} )




perform bayesian ensemble prediction.
#Arguments
- `predictions::Matrix{Float64}`: each column is the prediction of one hypothesis.
- `weights::Vector{Float64}`:     mixing weights.
#Return
- `Vector{Float64}`:              prediction y.

predictEnsemble( predictions::Vector{Matrix{Float64}}, weights::Vector{Float64} )

perform bayesian ensemble prediction. #Arguments

• predictions::Vector{Matrix{Float64}}: each matrix is the prediction of one hypothesis.
• weights::Vector{Float64}: mixing weights.

#Return

• Vector{Float64}: prediction y.

tobin( num::Int64 )