The Cross Entropy Objective is a widely used loss function in machine learning, particularly in the context of classification tasks. It quantifies the difference between two probability distributions: 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.
Mathematically, cross entropy is defined as:
H(p, q) = -Σ p(x) log(q(x))
where:
- 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) is the predicted probability of class labels output by the model.
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 multi-class classification problems.
Cross entropy is commonly employed in various machine learning frameworks and is particularly effective with neural networks when combined with softmax activation functions 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.