Binary Cross-Entropy Loss

A Binary Cross-Entropy Loss is a loss function that is a cross-entropy loss for binary classification or binary probability estimation.

• Context:
  • It can compute Binary Cross-Entropy Values as -[h log p + (1-h) log(1-p)].
  • It can serve as Binary Cross-Entropy Objective for maximum likelihood estimation.
  • It can handle Binary Cross-Entropy Weights for non-uniform sampling.
  • It can measure Binary Cross-Entropy Divergence between predicted and true probabilities.
  • ...
  • It can range from being an Unweighted Binary Cross-Entropy Loss to being a Weighted Binary Cross-Entropy Loss, depending on its binary cross-entropy sample weighting.
  • It can range from being a Simple Binary Cross-Entropy Loss to being a Regularized Binary Cross-Entropy Loss, depending on its binary cross-entropy complexity penalty.
  • ...
  • It can optimize Binary Cross-Entropy Parameters in models like Bradley-Terry Model.
  • It can provide Binary Cross-Entropy Gradients for optimization algorithms.
  • ...
• Example(s):
  • BT Model Binary Cross-Entropy Loss, for pairwise preference modeling.
  • Logistic Regression Binary Cross-Entropy Loss, for binary classification.
  • Neural Network Binary Cross-Entropy Loss, for output layer optimization.
  • ...
• Counter-Example(s):
  • Mean Squared Error Loss, which measures squared differences.
  • Multi-Class Cross-Entropy Loss, which handles multiple classes.
  • Hinge Loss, which uses margin-based formulation.
• See: Maximum Likelihood Estimation, Bradley-Terry Model, Probability Estimation.

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