Entropia Cruzada Binária, frequentemente abreviada como BCE, é uma função de perda amplamente utilizada função de perda in aprendizado de máquina, particularly in classificação binária tasks. It measures the dissimilarity between the true labels (0 or 1) and the predicted probabilities from a model. The goal of using Binary Cross-Entropy is to optimize the model’s predictions so that they closely match the actual outcomes.
A fórmula da Entropia Cruzada Binária é dada por:
- (y * log(p) + (1 - y) * log(1 - p))
where y is the true label (0 or 1), and p is the predicted probability that the output is 1. This function outputs a value between 0 and infinity, where a lower value indicates a better fit between the model’s predictions and the actual labels.
Na prática, a Entropia Cruzada Binária é usada em várias aplicações, como classificação de imagens, spam detection, and sentiment analysis. When training a model, the algoritmo de otimização seeks to minimize this loss function, thereby improving the accuracy of the predictions. The function is particularly useful because it provides a smooth gradient, which is essential for gradient-based optimization methods like stochastic gradient descent (SGD).
One important aspect of Binary Cross-Entropy is that it penalizes incorrect predictions more heavily when they are confident. For instance, if the model predicts a probability close to 1 for a classe negativa (label 0), it incurs a significant penalty, prompting the model to adjust its weights to reduce such confident but incorrect predictions in future iterations.