lossfunktion

LossFunktion is a mathematical construct used in machine learning to quantify how far a model’s predictions are from the observed targets. It serves as the objective that learning algorithms minimize during training. A loss function typically operates on a single example, producing a non-negative value L(y, ŷ) that is zero when the prediction matches the target according to the chosen criterion. The total loss on a dataset is the empirical risk, commonly computed as the average or sum of the pointwise losses across all examples.

Loss functions reflect the nature of the task. For regression, common choices include mean squared error (MSE), mean absolute error (MAE), and the robust Huber loss. For classification, widely used options include cross-entropy (log loss), binary logistic loss, and hinge loss. In probabilistic models, the loss often corresponds to the negative log-likelihood or related divergences such as the KL divergence. Additional specialized losses address issues like class imbalance (focal loss) or segmentation accuracy (Dice loss).

Properties of a good LossFunktion include non-negativity, a unique minimum at the desired target under the model class, and differentiability (or subdifferentiability) to enable gradient-based optimization. The loss function forms the basis for optimization algorithms such as gradient descent or Adam, which update model parameters to reduce the empirical risk. While the loss measures training error, evaluation metrics may differ and are used to assess generalization on unseen data.

In practice, the LossFunktion is chosen to match the task, data characteristics, and optimization considerations, often with regularization terms added to form a regularized objective.