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.
| Name | mail to: ( links ) |
|---|---|
| Yusei Fujimoto | yu25fujimoto"@"kandaquantum.co.jp ( Github Links ) |
- 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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