Method ComputeDualLoss

tensorflow/core/kernels/hinge-loss.h:75–84

Conjugate of hinge loss. This is computed as: \phi*(z) = z if z \in [-1, 0] and +infinity everywhere else. See for instance http://www.eecs.berkeley.edu/~wainwrig/stat241b/lec10.pdf Here we want the weighted version of the conjugate loss. It turns out, that if w is the weight of an example, the conjugate of the weighted hinge loss is given by: \phi*(z) = z if z \in [-w, 0] and +infinity everywhere

  // \phi_y*(z) = y*z if y*z \in [-w, 0] and +infinity everywhere else where
  // y \in {-1,1}. The following method implements \phi_y*(-\alpha/w).
  double ComputeDualLoss(const double current_dual, const double example_label,
                         const double example_weight) const final {
    // For binary classification, there are 2 conjugate functions, one per
    // label value (-1 and 1).
    const double y_alpha = current_dual * example_label;  // y \alpha
    if (y_alpha < 0 || y_alpha > 1.0) {
      return std::numeric_limits<double>::max();
    }
    return -y_alpha * example_weight;
  }

  // Hinge loss for binary classification for a single example. Hinge loss
  // equals max(0, 1 - y * wx) (see https://en.wikipedia.org/wiki/Hinge_loss).