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# Linear Regression Gradient Descent

Liner Regression with no reglarization

 ``` 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 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 StartChild : computation:Async<'T> * ?millisecondsTimeout:int -> Async<Async<'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