correct implementation of Hinge loss minimization

Question

I copied the hinge loss function from here (also LossC and LossFunc upon which it's based. Then I included it in my gradient descent algorithm like so:

  do 
  {
    iteration++;
    error = 0.0;
    cost = 0.0;

    //loop through all instances (complete one epoch)
    for (p = 0; p < number_of_files__train; p++) 
    {

      // 1. Calculate the hypothesis h = X * theta
      hypothesis = calculateHypothesis( theta, feature_matrix__train, p, globo_dict_size );

      // 2. Calculate the loss = h - y and maybe the squared cost (loss^2)/2m
      //cost = hypothesis - outputs__train[p];
      cost = HingeLoss.loss(hypothesis, outputs__train[p]);
      System.out.println( "cost " + cost );

      // 3. Calculate the gradient = X' * loss / m
      gradient = calculateGradent( theta, feature_matrix__train, p, globo_dict_size, cost, number_of_files__train);

      // 4. Update the parameters theta = theta - alpha * gradient
      for (int i = 0; i < globo_dict_size; i++) 
      {
          theta[i] = theta[i] - LEARNING_RATE * gradient[i];
      }

    }

    //summation of squared error (error value for all instances)
    error += (cost*cost);       

  /* Root Mean Squared Error */
  //System.out.println("Iteration " + iteration + " : RMSE = " + Math.sqrt( error/number_of_files__train ) );
  System.out.println("Iteration " + iteration + " : RMSE = " + Math.sqrt( error/number_of_files__train ) );

  } 
  while( error != 0 );

But this doesnt work at all. Is that due to the loss function? Maybe how I added the loss function to my code?

I guess it's also possible that my implementation of gradient descent is faulty.

Here are my methods for calculating the gradient and the hypothesis, are these right?

static double calculateHypothesis( double[] theta, double[][] feature_matrix, int file_index, int globo_dict_size )
{
    double hypothesis = 0.0;

     for (int i = 0; i < globo_dict_size; i++) 
     {
         hypothesis += ( theta[i] * feature_matrix[file_index][i] );
     }
     //bias
     hypothesis += theta[ globo_dict_size ];

     return hypothesis;
}

static double[] calculateGradent( double theta[], double[][] feature_matrix, int file_index, int globo_dict_size, double cost, int number_of_files__train)
{
    double m = number_of_files__train;

    double[] gradient = new double[ globo_dict_size];//one for bias?

    for (int i = 0; i < gradient.length; i++) 
    {
        gradient[i] = (1.0/m) * cost * feature_matrix[ file_index ][ i ] ;
    }

    return gradient;
}

The rest of the code is here if you're interested to take a look.

Below this sentence is what those loss functions look like. Should I use the loss or deriv, are these even correct?

/**
 * Computes the HingeLoss loss
 *
 * @param pred the predicted value
 * @param y the target value
 * @return the HingeLoss loss
 */
public static double loss(double pred, double y)
{
    return Math.max(0, 1 - y * pred);
}

/**
 * Computes the first derivative of the HingeLoss loss
 *
 * @param pred the predicted value
 * @param y the target value
 * @return the first derivative of the HingeLoss loss
 */
public static double deriv(double pred, double y)
{
    if (pred * y > 1)
        return 0;
    else
        return -y;
}

Answer 1

The code you provided for gradient does not look like a gradient of Hinge loss. Take a look at a valid equation, for example here: https://stats.stackexchange.com/questions/4608/gradient-of-hinge-loss