Support Interop between DiffSharp and MathNet and FSharp Stats For optimization Problems

[houstonhaynes]

Support Interop between DiffSharp and MathNet and FSharp Stats For optimization Problems

Issue #382 | Created by @AndyAbok | 2021-09-16 15:49:47 UTC |

if diffsharp could support interop between mathnet mostly for the the optimization module so as to take advantage of automatic differentiation capability for optimization problems.

#r "nuget: DiffSharp-lite,1.0.0-preview-781810429"
#r "nuget: MathNet.Numerics.FSharp"

open System
open MathNet.Numerics
open MathNet.Numerics.Optimization
open MathNet.Numerics.LinearAlgebra
open DiffSharp

let rosenbrockFunction (xs: Vector<float>) =
    let x, y = xs.[0], xs.[1]
    pown (1.0 - x) 2 + 100.0 * pown (y - pown x 2) 2

let gradient(x:Vector<float>) = 
    //redefine this funcion to consume tensor
    let rosenbrockGrad (x:Tensor) = 
        let x, y = x.[0], x.[1]
        pown (1.0 - x) 2 + 100.0 * pown (y - pown x 2) 2

    let toTensor = dsharp.tensor(x)
    let diffObjectiveFun = dsharp.grad rosenbrockGrad toTensor 
    //given it outputs a Tensor we can convert it to a vector given that's the input mathnet would need
    diffObjectiveFun |> vector


let LBFGS f grad initialVal =
    let objectiveFunction =
        new System.Func<Vector<float>,float>(f)
    
    let gradientFunction =
        new System.Func<Vector<float>,Vector<float>>(grad)
    
    let obj = ObjectiveFunction.Gradient(objectiveFunction,gradientFunction) 
    let solver =  LimitedMemoryBfgsMinimizer(1e-5, 1e-5, 1e-5, 5, 1000)   
    let result = solver.FindMinimum(obj,initialVal)
    result.MinimizingPoint   
    |> Vector.toSeq

let initialVal = [|0.0;0.0|] |> vector

let res = LBFGS rosenbrockFunction gradient initialVal'''

I think this would apply to Fsharp stats as well, as it also does use vectors in such kind of problems.

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Comment by @gbaydin | 2021-09-16 19:53:49 UTC

Hi @AndyAbok thanks for sharing this idea with some example code. Really helpful to understand how this type of scenario can work.