public void TestBackPropagationWithoutRegularisaion()
{
NeuralNetwork.CostFunctionWithThetaParameter backProp =
t =>
{
var backPropagationResult = NeuralNetwork.BackPropagation(Xm, ym, t, new List <int>()
{
4
}, 4, 0);
return(backPropagationResult);
};
var bothThetas = NeuralNetwork.PackThetas(new List <Matrix <double> >()
{
theta1NN, theta2NN
});
var resultNumericalGradient = NeuralNetwork.ComputeNumericalGradient(backProp, bothThetas);
var pathNumericalGradients = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\NumericalGradientForBackPropagationWithoutRegularisation.txt");
var matrixNumericalGradients = DelimitedReader.Read <double>(pathNumericalGradients);
Assert.IsTrue(MatricesEqual(resultNumericalGradient, matrixNumericalGradients));
var resultBackPropagation = NeuralNetwork.BackPropagation(Xm, ym, bothThetas, new List <int>()
{
4
}, 4, 0);
var pathGradientForBackPropagation = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\GradientForBackPropagationWithoutRegularisation.txt");
var matrixGradientForBackPropagation = DelimitedReader.Read <double>(pathGradientForBackPropagation);
Assert.IsTrue(Equalities.DoubleEquals(resultBackPropagation.Item1, 3.08744915815864));
Assert.IsTrue(MatricesEqual(resultBackPropagation.Item2, matrixGradientForBackPropagation));
Assert.IsTrue(MatricesEqual(resultBackPropagation.Item2, resultNumericalGradient, 0.000000001));
}
public static Tuple <Matrix <double>, Matrix <double> > GradientDescent(CostFunctionWithThetaParameter func,
Matrix <double> theta, double alpha, int numberIterations)
{
Stopwatch stopWatch = new Stopwatch();
stopWatch.Start();
Matrix <double> JHistory = new DenseMatrix(numberIterations, 1);
for (int i = 0; i < numberIterations; i++)
{
var res = func(theta);
var h = res.Item1;
var grad = res.Item2;
JHistory[i, 0] = h;
// "bold driver" - if we decrease the cost function, increase the learning rate by 5% but
// in case when we increase the cost function, decrease the learning rate by 50%
if (i > 0)
{
if (JHistory[i, 0] < JHistory[i - 1, 0])
{
alpha += (double)0.05 * alpha;
}
else
{
alpha -= (double)0.5 * alpha;
}
}
theta = theta - grad * alpha;
if (i > 0 && JHistory[i, 0] < JHistory[i - 1, 0] &&
Equalities.DoubleEquals(JHistory[i, 0], JHistory[i - 1, 0]))
{
break;
}
}
stopWatch.Stop();
// Get the elapsed time as a TimeSpan value.
TimeSpan ts = stopWatch.Elapsed;
// Format and display the TimeSpan value.
string elapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:00}",
ts.Hours, ts.Minutes, ts.Seconds, ts.Milliseconds / 10);
Console.WriteLine("RunTime " + elapsedTime);
return(Tuple.Create(theta, JHistory));
}
public void TestCostFunction()
{
var tupleJAndGrad = NeuralNetwork.CostFunction(theta, X, y);
var pathJ = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\J.txt");
var matrixJ = (DenseMatrix)DelimitedReader.Read <double>(pathJ);
var pathGrad = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\Grad.txt");
var matrixGrad = (DenseMatrix)DelimitedReader.Read <double>(pathGrad);
Assert.IsTrue(Equalities.DoubleEquals(tupleJAndGrad.Item1, matrixJ[0, 0]));
Assert.IsTrue(MatricesEqual(tupleJAndGrad.Item2, matrixGrad));
}
public void TestBackPropagationWithRegularisation()
{
NeuralNetwork.CostFunctionWithThetaParameter backProp =
t =>
{
var backPropagationResult = NeuralNetwork.BackPropagation(Xm, ym, t, new List <int>()
{
4
}, 4, 1);
return(backPropagationResult);
};
var bothThetas = NeuralNetwork.PackThetas(new List <Matrix <double> >()
{
theta1NN, theta2NN
});
var resultNumericalGradient = NeuralNetwork.ComputeNumericalGradient(backProp, bothThetas);
var pathNumericalGradients = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\NumericalGradients.txt");
var matrixNumericalGradients = DelimitedReader.Read <double>(pathNumericalGradients);
Assert.IsTrue(MatricesEqual(resultNumericalGradient, matrixNumericalGradients));
var resultBackPropagation = NeuralNetwork.BackPropagation(Xm, ym, bothThetas, new List <int>()
{
4
}, 4, 1);
var pathGradientForBackPropagation = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\GradientForBackPropagation.txt");
var matrixGradientForBackPropagation = DelimitedReader.Read <double>(pathGradientForBackPropagation);
Assert.IsTrue(Equalities.DoubleEquals(resultBackPropagation.Item1, 3.46051055642594));
Assert.IsTrue(MatricesEqual(resultBackPropagation.Item2, matrixGradientForBackPropagation));
Assert.IsTrue(MatricesEqual(resultBackPropagation.Item2, resultNumericalGradient, 0.000000001));
var resultGradientDescent = NeuralNetwork.GradientDescent(backProp, bothThetas, 1, 3000);
var pathResultTheta = Path.Combine(Utils.GetAssemblyPath(), "..\\..\\TestData\\ThetaAfterGradientDescentForBackProp.txt");
var matrixResultTheta = DelimitedReader.Read <double>(pathResultTheta);
Assert.IsTrue(MatricesEqual(resultGradientDescent.Item1, matrixResultTheta));
var resultCost = resultGradientDescent.Item2.ToRowWiseArray().LastOrDefault(elem => elem != 0.0d);
Assert.IsTrue(Equalities.DoubleEquals(resultCost, 2.2493405784756875));
}
public void TestGradientDescent()
{
Matrix <double> theta = new DenseMatrix(2, 1);
theta[0, 0] = 1;
theta[1, 0] = 1;
double alpha = 0.1;
int numIterations = 100;
var result = NeuralNetwork.GradientDescent(Equation, theta, alpha, numIterations);
var resultTheta = result.Item1;
Assert.IsTrue(Equalities.DoubleEquals(resultTheta[0, 0], 0, 0.00000001));
Assert.IsTrue(Equalities.DoubleEquals(resultTheta[1, 0], 0, 0.00000001));
var resultCost = result.Item2.ToRowWiseArray().LastOrDefault(elem => elem != 0.0d);
Assert.IsTrue(Equalities.DoubleEquals(resultCost, 0));
}