// compute the MCR on the test set
  private double GetMCRTestSet() {
    int numErrors = 0;

    for (int i = NTrain; i < NTrain + NTest; i++) {
      double label_i = Sigmoid.Calculate(Predict(i));

      if ((Y.get(i) == 1 && label_i < 0.5) || (Y.get(i) == 0 && label_i >= 0.5)) numErrors++;
    }

    return (double) numErrors / (double) NTest;
  }
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  // predict the label of the i-th instance
  public double PredictLabel(int i) {
    double label = 0;
    double maxConfidence = 0;

    for (int l = 0; l < numLabels; l++) {
      double confidence =
          Sigmoid.Calculate(MatrixUtilities.getRowByColumnProduct(S, i, W, l)); // + biasW[l]);

      if (confidence > maxConfidence) {
        maxConfidence = confidence;
        label = (double) l;
      }
    }

    return label;
  }
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  // get the log loss of the target prediction
  public double GetLossY(int startIndex, int endIndex) {
    double YTrainLoss = 0;
    int numObservedCells = 0;

    for (int i = startIndex; i < endIndex; i++)
      for (int l = 0; l < numLabels; l++)
        if (YExtended.get(i, l) != GlobalValues.MISSING_VALUE) {
          double y_hat_i =
              Sigmoid.Calculate(
                  MatrixUtilities.getRowByColumnProduct(S, i, W, l)); // + biasW[l]);
          double y_i = YExtended.get(i, l);

          YTrainLoss += -y_i * Math.log(y_hat_i) - (1 - y_i) * Math.log(1 - y_hat_i);

          numObservedCells++;
        }

    return YTrainLoss / (double) numObservedCells;
  }
  public void LearnLA(boolean updateOnlyW) {
    if (beta == 1) return;

    double e_i = 0, F_ik = 0;
    double regWConst = (2 * lambdaW) / NTrain;

    for (int i = 0; i < NTrain; i++) {
      e_i = Y.get(i) - Sigmoid.Calculate(Predict(i));

      for (int k = 0; k < K; k++) {
        F_ik = 0;

        for (int j = 0; j < NSegments; j++) {
          D[i][j][k] -= eta * ((1 - beta) * -2 * e_i * W[k] + lambdaD * D[i][j][k]);

          F_ik += D[i][j][k];
        }

        W[k] -= eta * ((1 - beta) * -2 * e_i * F_ik + regWConst * W[k]);
      }
    }
  }
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  public double Optimize() {
    // initialize the data structures
    Initialize();

    Random rand = new Random();

    double prevLossH = Double.MAX_VALUE;

    int YUpdatefrequency = HObserved.size() / numTotalInstances, i, l, idxY = 0;

    for (int epoch = 0; epoch < maxEpochs; epoch++) {
      // update H loss
      if (alphaH > 0) {
        double err_il;

        for (int idx = 0; idx < HObserved.size(); idx++) {
          i = HObserved.get(idx).row;
          l = HObserved.get(idx).col;

          err_il = H.cells[i][l] - MatrixUtilities.getRowByColumnProduct(S, i, P, l) - biasP[l];

          for (int k = 0; k < D; k++) {
            S.cells[i][k] -= eta * (-2 * alphaH * err_il * P.cells[k][l] + lambdaS * S.cells[i][k]);
            P.cells[k][l] -= eta * (-2 * alphaH * err_il * S.cells[i][k] + lambdaP * P.cells[k][l]);
          }

          biasP[l] -= eta * (-2 * alphaH * err_il);

          if (idx % YUpdatefrequency == 0) {
            if (alphaY > 0) {
              i = YObserved.get(idxY).row;
              l = YObserved.get(idxY).col;

              double err_i =
                  YExtended.cells[i][l]
                      - Sigmoid.Calculate(
                          MatrixUtilities.getRowByColumnProduct(S, i, W, l)); // + biasW[l]);

              for (int k = 0; k < D; k++) {
                S.cells[i][k] -= eta * (alphaY * -err_i * W.cells[k][l] + lambdaS * S.cells[i][k]);
                W.cells[k][l] -= eta * (alphaY * -err_i * S.cells[i][k] + lambdaW * W.cells[k][l]);
              }

              biasW[l] -= eta * (-alphaY * err_i);

              idxY = (idxY + 1) % YObserved.size();
            }
          }
        }
      }

      double lossH = GetLossH();

      if (epoch % 3 == 0) {
        // compute the losses of each relation and print the result
        double lossYTrain = GetLossY(0, numTrainInstances),
            lossYTest = GetLossY(numTrainInstances, numTotalInstances),
            mcrTrain = GetErrorRate(0, numTrainInstances),
            mcrTest = GetErrorRate(numTrainInstances, numTotalInstances),
            mcrNN = GetTestErrorNN();

        Logging.println(
            "Epoch="
                + df.format(epoch)
                + ", Eta="
                + df.format(eta)
                + ", LH="
                + df.format(lossH)
                + ", LY="
                + df.format(lossYTrain)
                + "/"
                + df.format(lossYTest)
                + ", MCR="
                + df.format(mcrTrain)
                + "/"
                + df.format(mcrTest)
                + "/"
                + df.format(mcrNN),
            LogLevel.DEBUGGING_LOG);

        // Logging.println("LX="+lossX+", LH="+lossH + ", LY="+lossY+", MCR=["+
        // mcrTrain+","+mcrTest+"]", LogLevel.DEBUGGING_LOG);
      }

      if (lossH < prevLossH) {
        // eta *= 1.01;

        prevLossH = lossH;
      } else {
        // eta *= 0.7;
      }
    }

    // return the ultimate MCR
    return GetErrorRate(numTrainInstances, numTotalInstances);
    // return GetTestErrorNN();
  }
  // compute the accuracy loss of instance i according to the
  // smooth hinge loss
  public double AccuracyLoss(int i) {
    double Y_hat_i = Predict(i);
    double sig_y_i = Sigmoid.Calculate(Y_hat_i);

    return -Y.get(i) * Math.log(sig_y_i) - (1 - Y.get(i)) * Math.log(1 - sig_y_i);
  }