InverseIsing.jl

Inverse Ising inference for General Boltzmann Machines [GBM].

The inverse Ising problem is to estimate the spin-spin interaction from the spin configurations. InverseIsing.jl, based on julia language, contains a machine for generating spin configurations (Simulated Annealing Machine:SA) and a solver for the inverse ising problem.

Pkg.add("InverseIsing")

For ising case, input the magnetic field h and interaction J.

julia> using InverseIsing

julia> h = Dict(1 => -1) # Longitudinal magnetic field

julia> J = Dict((1, 2) => 1) # Ferromagnetic-bond

julia> result = anneal(h, J)

The result of the annealing is output to the response structure.

julia> result.states
1-element Array{Array{Int64,1},1}:
 [-1, -1]

Train GBM parameters:

julia> using InverseIsing

julia> samples = [1 -1 -1;] # Spin configuration sample.

julia> model = GBM(3) # Set the number of units.

julia> fit(model, samples)

After model is fitted, you can estimate GBM parameters known as weights:

julia> W = infer(model)
3×3 Array{Int64,2}:
  0  -1  -1
 -1   0   1
 -1   1   0

The output can be transformed to make the display easier to read:

julia> decode(W)
OrderedCollections.OrderedDict{Tuple{Int64,Int64},Int64} with 3 entries:
  (1, 2) => -1
  (1, 3) => -1
  (2, 3) => 1

The above example means that the interaction between (1, 2) and (1, 3) is antiferromagnetic bond and only (2, 3) is ferromagnetic bond.

• S. Kirkpatrick and C. D. Gelatt and M. P. Vecchi, Science 220, 671 (1983)
• E. Aurell and M. Ekeberg, Phys. Rev. Lett. 108, 090201 (2012)

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