Fundamentals
Entropy
Entropy, in the context of information theory, quantifies the uncertainty or randomness associated with a random variable. It measures the average amount of information needed to describe the outcome of that variable; higher entropy implies greater unpredictability.
Explanation
In machine learning, entropy is frequently used as a measure of impurity or disorder within a dataset. Specifically, it plays a critical role in decision tree algorithms to determine the optimal split criteria. When training a decision tree, the goal is to reduce entropy at each node by partitioning the data into subsets that are more homogeneous with respect to the target variable. The information gain, which is the reduction in entropy after a split, is often used to select the best attribute for splitting. Cross-entropy is another important application, which quantifies the difference between two probability distributions. This is widely used as a loss function for classification tasks, especially in neural networks, where the goal is to minimize the cross-entropy between the predicted probability distribution and the true distribution of class labels.