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Showing content from http://accord-framework.net/docs/html/T_Accord_Statistics_Models_Regression_NonlinearRegression.htm below:

Nonlinear Regression.

Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0

[SerializableAttribute]
public class NonlinearRegression : TransformBase<double[], double>, 
	ICloneable

<SerializableAttribute>
Public Class NonlinearRegression
	Inherits TransformBase(Of Double(), Double)
	Implements ICloneable

The NonlinearRegression type exposes the following members.

Creates a new object that is a copy of the current instance.

Computes the model output for the given input vector.

Determines whether the specified object is equal to the current object.

Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.

Serves as the default hash function.

Gets the Type of the current instance.

Creates a shallow copy of the current Object.

Returns a string that represents the current object.

Applies the transformation to a set of input vectors, producing an associated set of output vectors.

Applies the transformation to an input, producing an associated output.

Applies the transformation to an input, producing an associated output.

Checks whether an object implements a method with the given name.

Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.

Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.

Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.

The first example shows how to fit a non-linear regression with LevenbergMarquardt.

double[,] data =
{
    { -40,    -21142.1111111111 },
    { -30,    -21330.1111111111 },
    { -20,    -12036.1111111111 },
    { -10,      7255.3888888889 },
    {   0,     32474.8888888889 },
    {  10,     32474.8888888889 },
    {  20,      9060.8888888889 },
    {  30,    -11628.1111111111 },
    {  40,    -15129.6111111111 },
};


double[][] inputs = data.GetColumn(0).ToJagged();
double[] outputs = data.GetColumn(1);


var nls = new NonlinearLeastSquares()
{
    NumberOfParameters = 3,

    
    StartValues = new[] { 4.2, 0.3, 1 },

    
    Function = (w, x) => w[0] * x[0] * x[0] + w[1] * x[0] + w[2],

    
    Gradient = (w, x, r) =>
    {
        r[0] = w[0]* w[0]; 
        r[1] = w[0];       
        r[2] = 1;          
    },

    Algorithm = new LevenbergMarquardt()
    {
        MaxIterations = 100,
        Tolerance = 0
    }
};


var regression = nls.Learn(inputs, outputs);


double[] predict = regression.Transform(inputs);

Dim data(,) As Double =
{
    {-40, -21142.1111111111},
    {-30, -21330.1111111111},
    {-20, -12036.1111111111},
    {-10, 7255.3888888889},
    {0, 32474.8888888889},
    {10, 32474.8888888889},
    {20, 9060.8888888889},
    {30, -11628.1111111111},
    {40, -15129.6111111111}
}


Dim inputs As Double()() = data.GetColumn(0).ToJagged()
Dim outputs As Double() = data.GetColumn(1)


Dim nls As NonlinearLeastSquares = New NonlinearLeastSquares
With nls
    .NumberOfParameters = 3

    
    .StartValues = {4.2, 0.3, 1}

    
    .Function = Function(w, x) w(0) * x(0) * x(0) + w(1) * x(0) + w(2)

    
    .Gradient = Sub(w, x, r)
                    r(0) = 2 * w(0) 
                    r(1) = w(1)     
                    r(2) = w(2)     
                End Sub
End With

Dim algorithm As LevenbergMarquardt = New LevenbergMarquardt
With algorithm
    .MaxIterations = 100
    .Tolerance = 0
End With

nls.Algorithm = algorithm

Dim regression As NonlinearRegression = nls.Learn(inputs, outputs)


Dim predict As Double() = regression.Transform(inputs)

The second example shows how to fit a non-linear regression with GaussNewton.

double[,] data =
{
    { 0.03, 0.1947, 0.425, 0.626, 1.253, 2.500, 3.740 },
    { 0.05, 0.127, 0.094, 0.2122, 0.2729, 0.2665, 0.3317}
};


double[][] inputs = data.GetRow(0).ToJagged();
double[] outputs = data.GetRow(1);


var nls = new NonlinearLeastSquares()
{
    
    StartValues = new[] { 0.9, 0.2 },

    
    Function = (w, x) => (w[0] * x[0]) / (w[1] + x[0]),

    
    Gradient = (w, x, r) =>
    {
        r[0] = -((-x[0]) / (w[1] + x[0]));
        r[1] = -((w[0] * x[0]) / Math.Pow(w[1] + x[0], 2));
    },

    Algorithm = new GaussNewton()
    {
        MaxIterations = 0,
        Tolerance = 1e-5
    }
};


var regression = nls.Learn(inputs, outputs);


double[] predict = regression.Transform(inputs);

Dim data As Double(,) =
{
    {0.03, 0.1947, 0.425, 0.626, 1.253, 2.5, 3.74},
    {0.05, 0.127, 0.094, 0.2122, 0.2729, 0.2665, 0.3317}
}


Dim inputs As Double()() = data.GetRow(0).ToJagged()
Dim outputs As Double() = data.GetRow(1)


Dim nls As NonlinearLeastSquares = New NonlinearLeastSquares
With nls
    
    .StartValues = {0.9, 0.2}

    
    .Function = Function(w, x) w(0) * x(0) / (w(1) + x(0))

    
    .Gradient = Sub(w, x, r)
                    r(0) = -((-x(0)) / (w(1) + x(0)))
                    r(1) = -((w(0) * x(0)) / System.Math.Pow(w(1) + x(0), 2))
                End Sub
End With

Dim algorithm As GaussNewton = New GaussNewton
With algorithm
    .MaxIterations = 0
    .Tolerance = 0.00001
End With

nls.Algorithm = algorithm

Dim regression As NonlinearRegression = nls.Learn(inputs, outputs)


Dim predict As Double() = regression.Transform(inputs)

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