Ristiinentropiaa

Ristiinentropiaa is a Finnish term that translates to "cross-entropy" in English. It is a fundamental concept in information theory and machine learning. Cross-entropy measures the difference between two probability distributions. Specifically, it quantifies how well one probability distribution predicts another.

In machine learning, cross-entropy is commonly used as a loss function. When training a classification model, the goal is to minimize the cross-entropy between the true distribution of the data labels and the distribution predicted by the model. A lower cross-entropy value indicates that the model's predictions are closer to the actual labels, suggesting better performance.

The formula for cross-entropy for discrete probability distributions P and Q is given by H(P, Q) = - Σ P(x) log Q(x), where the sum is over all possible outcomes x. In practice, P often represents the true distribution (e.g., one-hot encoded labels) and Q represents the model's predicted probabilities.

Cross-entropy is closely related to Kullback-Leibler (KL) divergence, another measure of the difference between probability distributions. In fact, KL divergence can be expressed as the difference between cross-entropy and the entropy of the true distribution: D_KL(P || Q) = H(P, Q) - H(P). Therefore, minimizing cross-entropy is equivalent to minimizing KL divergence when the true distribution P is fixed. This metric is widely applied in tasks such as binary classification, multi-class classification, and deep learning models.