Which of the following is used as the cost function for training a logistic regression model?

In logistic regression, the cost function that is most appropriate for training the model is log loss, also known as binary cross-entropy loss. This function is specifically designed for binary classification problems, which is the primary application of logistic regression.

Log loss quantifies the difference between the predicted probabilities of the positive class and the actual outcomes. It penalizes wrong predictions more heavily when the confidence level of the prediction is high. Therefore, the log loss function effectively ensures that the model not only aims to predict the correct class but also evaluates the certainty of these predictions, which is crucial in applications where probabilities are interpreted as confidence levels in the classifications.

In contrast, while mean absolute error (MAE) and mean squared error (MSE) are commonly used in regression problems where the outputs are continuous values, they are not suitable for a model that outputs probabilities as logistic regression does. The normal function is not a recognized cost function in the context of training logistic regression. This specificity of log loss makes it the optimal choice for evaluating a logistic regression model's performance during training.