Linear Regression Gradient Descent

 1: 
 2: 
 3: 
 4: 
 5: 
 6: 
 7: 
 8: 
 9: 
10: 
11: 
12: 
13: 
14: 
15: 
16: 
17: 
18: 
19: 
20: 
21: 
22: 
23: 
24: 
25: 
26: 
27: 
28: 
29: 
30: 
31: 
32: 
33: 
34: 
35: 
36: 
37: 
38: 
39: 
40: 
41: 

open MathNet.Numerics.LinearAlgebra.Double

let gds_orig (X: Matrix) (y: Vector) (th: Vector) (alp: float) =
  let m = y.Count  
  let n = X.ColumnCount
  let mf = float m
  let oldth = th.Clone()
  for j = 0 to n - 1 do 
    printfn "Regression for feature: %i" j
    let acc = 
      [| 
        for i = 1 to m - 1 do 
          yield async { 
            return ((X.Row(i) * oldth) - y.[i]) * (X.[i,j]) 
          }     
      |] |> Async.Parallel |> Async.RunSynchronously
         |> Array.sum
         |> (fun acc -> acc * (alp / mf))
    do th.[j] <- oldth.[j] - acc 
  th

let gds_fun (X: Matrix) (y: Vector) (th: Vector) (alp: float) =
  th |> Vector.mapi (fun j v -> 
     printfn "Feature: %i" j
     let acc = 
        X |> Matrix.sumRowsBy 
              (fun i xr -> (xr * th - y.[i]) * X.[i,j])
          |> (fun acc -> acc * (alp / float y.Count))
     in v - acc)

// Tweet Sized!
let gds_golf (X: Matrix) (y: Vector) (θ: Vector) (α: float) =
  θ |> Vector.mapi (fun j v -> 
    v - (X |> Matrix.sumRowsBy (fun i xr -> 
      (xr * θ - y.[i]) * X.[i,j]) 
      |> (*) (α / float y.Count)))

            
// Tweet sized with words!
let gds_vec (X: Matrix) (y: Vector) (θ: Vector) (α: float) =
    θ - ((X * θ - y) * X * (α / float y.Count))

namespace MathNet

namespace MathNet.Numerics

namespace MathNet.Numerics.LinearAlgebra

namespace MathNet.Numerics.LinearAlgebra.Double

val gds_orig : X:Matrix -> y:Vector -> th:Vector -> alp:float -> Vector

Full name: Script.gds_orig

val X : Matrix

type Matrix =
  inherit Matrix<float>
  member Cholesky : unit -> Cholesky<float>
  member CoerceZero : threshold:float -> unit
  member ColumnAbsoluteSums : unit -> Vector<float>
  member ColumnNorms : norm:float -> Vector<float>
  member ColumnSums : unit -> Vector<float>
  member ConjugateTranspose : unit -> Matrix<float>
  member Evd : ?symmetricity:Symmetricity -> Evd<float>
  member FrobeniusNorm : unit -> float
  member GramSchmidt : unit -> GramSchmidt<float>
  member InfinityNorm : unit -> float
  ...

Full name: MathNet.Numerics.LinearAlgebra.Double.Matrix

val y : Vector

type Vector =
  inherit Vector<float>
  member AbsoluteMaximum : unit -> float
  member AbsoluteMaximumIndex : unit -> int
  member AbsoluteMinimum : unit -> float
  member AbsoluteMinimumIndex : unit -> int
  member CoerceZero : threshold:float -> unit
  member InfinityNorm : unit -> float
  member L1Norm : unit -> float
  member L2Norm : unit -> float
  member MaximumIndex : unit -> int
  member MinimumIndex : unit -> int
  ...

Full name: MathNet.Numerics.LinearAlgebra.Double.Vector

val th : Vector

val alp : float

Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>

val m : int

property MathNet.Numerics.LinearAlgebra.Vector.Count: int

val n : int

property MathNet.Numerics.LinearAlgebra.Matrix.ColumnCount: int

val mf : float

val oldth : MathNet.Numerics.LinearAlgebra.Vector<float>

MathNet.Numerics.LinearAlgebra.Vector.Clone() : MathNet.Numerics.LinearAlgebra.Vector<float>

val j : int

val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn

val acc : float

val i : int

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

MathNet.Numerics.LinearAlgebra.Matrix.Row(index: int) : MathNet.Numerics.LinearAlgebra.Vector<float>
MathNet.Numerics.LinearAlgebra.Matrix.Row(index: int, result: MathNet.Numerics.LinearAlgebra.Vector<float>) : unit
MathNet.Numerics.LinearAlgebra.Matrix.Row(rowIndex: int, columnIndex: int, length: int) : MathNet.Numerics.LinearAlgebra.Vector<float>
MathNet.Numerics.LinearAlgebra.Matrix.Row(rowIndex: int, columnIndex: int, length: int, result: MathNet.Numerics.LinearAlgebra.Vector<float>) : unit

Multiple items
type Async
static member AsBeginEnd : computation:('Arg -> Async<'T>) -> ('Arg * AsyncCallback * obj -> IAsyncResult) * (IAsyncResult -> 'T) * (IAsyncResult -> unit)
static member AwaitEvent : event:IEvent<'Del,'T> * ?cancelAction:(unit -> unit) -> Async<'T> (requires delegate and 'Del :> Delegate)
static member AwaitIAsyncResult : iar:IAsyncResult * ?millisecondsTimeout:int -> Async<bool>
static member AwaitTask : task:Task<'T> -> Async<'T>
static member AwaitWaitHandle : waitHandle:WaitHandle * ?millisecondsTimeout:int -> Async<bool>
static member CancelDefaultToken : unit -> unit
static member Catch : computation:Async<'T> -> Async<Choice<'T,exn>>
static member FromBeginEnd : beginAction:(AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromBeginEnd : arg:'Arg1 * beginAction:('Arg1 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromBeginEnd : arg1:'Arg1 * arg2:'Arg2 * beginAction:('Arg1 * 'Arg2 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromBeginEnd : arg1:'Arg1 * arg2:'Arg2 * arg3:'Arg3 * beginAction:('Arg1 * 'Arg2 * 'Arg3 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromContinuations : callback:(('T -> unit) * (exn -> unit) * (OperationCanceledException -> unit) -> unit) -> Async<'T>
static member Ignore : computation:Async<'T> -> Async<unit>
static member OnCancel : interruption:(unit -> unit) -> Async<IDisposable>
static member Parallel : computations:seq<Async<'T>> -> Async<'T []>
static member RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:CancellationToken -> 'T
static member Sleep : millisecondsDueTime:int -> Async<unit>
static member Start : computation:Async<unit> * ?cancellationToken:CancellationToken -> unit
static member StartAsTask : computation:Async<'T> * ?taskCreationOptions:TaskCreationOptions * ?cancellationToken:CancellationToken -> Task<'T>
static member StartChild : computation:Async<'T> * ?millisecondsTimeout:int -> Async<Async<'T>>
static member StartChildAsTask : computation:Async<'T> * ?taskCreationOptions:TaskCreationOptions -> Async<Task<'T>>
static member StartImmediate : computation:Async<unit> * ?cancellationToken:CancellationToken -> unit
static member StartWithContinuations : computation:Async<'T> * continuation:('T -> unit) * exceptionContinuation:(exn -> unit) * cancellationContinuation:(OperationCanceledException -> unit) * ?cancellationToken:CancellationToken -> unit
static member SwitchToContext : syncContext:SynchronizationContext -> Async<unit>
static member SwitchToNewThread : unit -> Async<unit>
static member SwitchToThreadPool : unit -> Async<unit>
static member TryCancelled : computation:Async<'T> * compensation:(OperationCanceledException -> unit) -> Async<'T>
static member CancellationToken : Async<CancellationToken>
static member DefaultCancellationToken : CancellationToken

Full name: Microsoft.FSharp.Control.Async

--------------------
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

module Array

from Microsoft.FSharp.Collections

val sum : array:'T [] -> 'T (requires member ( + ) and member get_Zero)

Full name: Microsoft.FSharp.Collections.Array.sum

val gds_fun : X:Matrix -> y:Vector -> th:Vector -> alp:float -> 'a

Full name: Script.gds_fun

val gds_golf : X:Matrix -> y:Vector -> θ:Vector -> α:float -> 'a

Full name: Script.gds_golf

val θ : Vector

val α : float

val gds_vec : X:Matrix -> y:Vector -> θ:Vector -> α:float -> MathNet.Numerics.LinearAlgebra.Vector<float>

Full name: Script.gds_vec