Das Kreuz Entropie Ziel is a widely used Verlustfunktion in maschinellem Lernen, particularly in the context of classification tasks. It quantifies the difference between two Wahrscheinlichkeitsverteilungen: the true distribution of labels and the predicted distribution output by a model. The objective is to minimize this difference, which represents how well the model’s predictions align with the actual labels.
Mathematisch ist die Kreuzentropie definiert als:
H(p, q) = -Σ p(x) log(q(x))
wobei:
- H(p, q) is the cross entropy between the true distribution p and the predicted distribution q.
- p(x) is the true probability of class labels (usually represented as one-hot encoded vectors).
- q(x) ist die vom Modell vorhergesagte Wahrscheinlichkeit der Klassenlabels.
In practical terms, when using cross entropy as the objective function, the model is penalized more heavily for confident but incorrect predictions. This characteristic makes it especially effective for tasks where accurate probability estimation is critical, such as in Mehrklassenklassifikation Probleme.
Cross entropy is commonly employed in various machine learning frameworks and is particularly effective with neural networks when combined with softmax Aktivierungsfunktionen in the output layer. The optimization process adjusts the model parameters to minimize the cross entropy loss, thereby improving the model’s accuracy and reliability in predicting outcomes.