/// <summary>
///
/// </summary>
/// <param name="theta"></param>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="lambda"></param>
/// <returns>Item1 - cost, Item2 - grad</returns>
public Tuple <double, double[]> CostFunction()
{
int m = y.Length;
int n = Theta.Length;
double[] one_minus_y = MLMath.ItemCalculate(1, y, (a, b) => a - b);
double[] h = H();
double[] log_h = MLMath.ItemCalculate(h, i => Math.Log(i));
double[] one_minus_h = MLMath.ItemCalculate(1, h, (a, b) => a - b);
double[] log_1_minus_h = MLMath.ItemCalculate(one_minus_h, i => Math.Log(i));
double cost = (1.0 / m) * (-MLMath.ItemMultiplyAndSum(y, log_h) - MLMath.ItemMultiplyAndSum(one_minus_y, log_1_minus_h));
//Regularization
double[] theta_reg = new double[n];
theta_reg[0] = 0;
for (int i = 1; i < n; i++)
{
theta_reg[i] = Theta[i];
}
double reg = Lambda / (2 * m) * (MLMath.ItemMultiplyAndSum(theta_reg, theta_reg));
cost += reg;
//Gradient
double[] grad = new double[n];
for (int i = 0; i < n; i++)
{
double[] x_i_vector = MLMath.GetVector(x, 1, i);
grad[i] = -Alpha * ((1.0 / m) * MLMath.ItemMultiplyAndSum(x_i_vector, MLMath.Minus(h, y)) + Lambda / m * theta_reg[i]);
}
return(new Tuple <double, double[]>(cost, grad));
}
public double[] H()
{
int m = x.GetLength(0);
double[] z = new double[m];
for (int i = 0; i < m; i++)
{
double[] x_vector = MLMath.GetVector(x, 0, i);
z[i] = MLMath.ItemMultiplyAndSum(Theta, x_vector);
}
return(MLMath.ItemCalculate(z, c => MLMath.Sigmoid(c)));
}