When dealing with binary targets, what type of likelihood function is used in neural network regressions?

In the context of neural network regressions for binary targets, the likelihood function focuses on maximizing the probability of the observed outcomes given the model parameters. This is based on the principles of maximum likelihood estimation (MLE), which aims to find the parameter values that make the observed data most probable.

For binary targets, the probability of each class can be modeled using the logistic function, which transforms the linear combination of inputs through the neural network layers into a probability score. The likelihood function, in this case, involves calculating the likelihood of observing the provided binary data under the model's predictions. The goal is to adjust the network's parameters to maximize this likelihood, thereby improving the model's predictive performance on unseen data.

Other approaches, such as standard, minimum, and marginal likelihood functions, do not apply directly in this context as they do not focus on maximizing the probability of observed outcomes in a manner appropriate for binary classification tasks. Standard likelihood might be too broad or not explicitly defined in binary models, while minimum and marginal likelihoods do not align with the objective of optimizing the binary classification framework.