Method getM_Bar_for_w0

JSAT/src/jsat/classifiers/linear/NewGLMNET.java:839–882

When we perform a warm start, we want to train to the same point that we would have if we had not done a warm start. But our stopping point is based on the initial relative error. To get around that, this method computes what the error would have been for the zero weight vector @param n @param l @pa

(int n, int l, List<Vec> columnsOfX, double[] col_neg_class_sum, double col_neg_class_sum_bias)

     * @return the error for M_bar that would have been computed if we were using the zero weight vector
     */
    private double getM_Bar_for_w0(int n, int l, List<Vec> columnsOfX, double[] col_neg_class_sum, double col_neg_class_sum_bias)
    {
        /**
         * if w=0, then D_part[i] = 0.5 for all i
         */
        final double D_part_i = 0.5;
        
        
        //algo 3, Step 1.
        double M_bar = 0;
        //algo 3, Step 2. 
        for(int j = 0; j < n; j++)
        {
            final double w_j = 0;

            //2.1. Calculate H^k_{jj}, ∇_j L(w^k) and ∇^S_j f(w^k)
            double delta_j_L = -columnsOfX.get(j).sum()*0.5;

            delta_j_L = /* (l2w * w_j) not needed b/c w_j=0*/ + C * (delta_j_L + col_neg_class_sum[j]);

            double deltaS_j_fw;
            //only the w_j = 0 case applies, b/c that is what this method is for!             
            //w_j = 0
            deltaS_j_fw = signum(delta_j_L) * max(abs(delta_j_L) - alpha, 0);
            //done with step 2, we have all the info
            M_bar += abs(deltaS_j_fw);

        }

        if (useBias)
        {
            //2.1. Calculate H^k_{jj}, ∇_j L(w^k) and ∇^S_j f(w^k)
            double delta_j_L = 0;

            for (int i = 0; i < l; i++)//all have an implicit bias term
                delta_j_L += -D_part_i;
            delta_j_L = C * (delta_j_L + col_neg_class_sum_bias);
            
            double deltaS_j_fw = delta_j_L;
            
            M_bar += abs(deltaS_j_fw);
        }
        return M_bar;
    }