CsminWel.jl

Interface to Chris Sims' csminwel optimization code. The code borrows from DSGE.jl, but it is adapted to be compatibles with the Optim.jl's API. When the derivative of the minimand is not supply either Finite Difference of Forward Automatic Differentiation derivatives are automatically supplied to the underlying code.

Differently from the solver in Optim.jl, Csminwel returns an estimate of the inverse of the Hessian at the solution.

#=
Maximizing loglikelihood logistic models
=#
using StatsFuns
srand(1)
x = [ones(200) randn(200,4)]
y = [rand() < 0.5 ? 1. : 0. for j in 1:200]

function loglik(beta)
    xb = x*beta
    sum(-y.*xb + log1pexp.(xb))
end

function dloglik(beta)
    xb = x*beta
    px = logistic.(xb)
    -x'*(y.-px)
end

function fg!(beta, stor)
    stor[:] = dloglik(beta)
end

## With analytical derivative
res1 = optimize(loglik, fg!, zeros(5), BFGS())
res2 = optimize(loglik, fg!, zeros(5), Csminwel())

## With finite-difference derivative
res3 = optimize(loglik, zeros(5), Csminwel())

## With forward AD derivative
res4 = optimize(loglik, zeros(5), Csminwel(), OptimizationOptions(autodiff=true))

## inverse Hessian
res2.invH