What is a common cost function used to evaluate performance in multinomial logistic regression?

The cross-entropy loss function, often referred to simply as "cross-entropy," is indeed a common cost function used in multinomial logistic regression. This function measures the dissimilarity between the true distribution of the labels and the predicted probabilities outputted by the model. In the context of multinomial logistic regression, where the aim is to classify instances into multiple possible categories, cross-entropy provides a way to quantify how well the model’s predictions align with the actual class labels.

When a model predicts a probability distribution over classes for a given instance, cross-entropy effectively penalizes incorrect predictions more heavily, particularly when the predicted probability for the true class is low. The formula for cross-entropy involves taking the negative log of the predicted probability for the true class, which reinforces the idea that the model should ideally assign a high probability to the true class. This characteristic makes cross-entropy particularly effective for training models on classification tasks, including multinomial logistic regression.

In contrast, while log loss is also a term used in the context of logistic regression to describe a similar concept, it generally refers to binary cases. The cluster sum of squares is more relevant in unsupervised learning contexts, such as clustering, where the goal is to minimize the variance within