Cross-Entropy Loss

What is Cross-Entropy Loss? Cross-Entropy Loss Explained.

Cross-entropy loss, also known as log loss or logistic loss, is a common loss function used in classification tasks, particularly in machine learning models that employ logistic regression or softmax activation.

Here are some key points to understand about cross-entropy loss:

Cross-entropy loss measures the dissimilarity between predicted probabilities and the true class labels. It quantifies the difference between the predicted probability distribution and the actual distribution of the target variable.

Binary Cross-Entropy Loss: In binary classification tasks, where there are two mutually exclusive classes (e.g., class 0 and class 1), the binary cross-entropy loss is commonly used. It calculates the loss for each example individually and then averages the losses across all examples. The formula for binary cross-entropy loss is:

Cross-entropy loss = -(y * log(p) + (1 – y) * log(1 – p))

Here, y represents the true class label (0 or 1), and p represents the predicted probability of the positive class.

Categorical Cross-Entropy Loss: In multi-class classification tasks, where there are more than two classes, the categorical cross-entropy loss is used. It extends the binary cross-entropy loss to handle multiple classes by summing the losses for each class. The formula for categorical cross-entropy loss is:

Cross-entropy loss = -Σ(y * log(p))

Here, y is a one-hot encoded vector representing the true class label, and p is a vector of predicted probabilities for each class.

Interpretation: The cross-entropy loss is a measure of how well the predicted probabilities match the true class labels. It penalizes large differences between the predicted probabilities and the actual values, assigning higher losses when the predictions are far from the true labels. The loss is minimized when the predicted probabilities align perfectly with the true class distributions.

Optimization: The goal of training a model is to minimize the cross-entropy loss by adjusting the model’s parameters. Optimization algorithms, such as gradient descent or its variants, are used to update the model’s parameters iteratively, aiming to find the parameter values that minimize the loss.

Applications: Cross-entropy loss is widely used in various classification tasks, including image classification, text classification, sentiment analysis, and multi-label classification. It is commonly used in models that employ logistic regression, sigmoid activation, or softmax activation functions.

It’s worth noting that cross-entropy loss is just one of many possible loss functions used in classification tasks. Its choice depends on the specific problem and the nature of the target variable. Cross-entropy loss is popular because it encourages models to produce well-calibrated probabilities and provides efficient gradients for optimization.