# Why is cross entropy based on Bernoulli or Multinoulli probability distribution?

When we use logistic regression, we use cross entropy as the loss function. However, based on my understanding and https://machinelearningmastery.com/cross-entropy-for-machine-learning/, cross entropy evaluates if two or more distributions are similar to each other. And the distributions are assumed to be Bernoulli or Multinoulli.

So, my question is: why we can always use cross entropy, i.e., Bernoulli in regression problems? Does the real values and the predicted values always follow such distribution?

Background:
The concept of Cross Entropy is inherited from Information theory where it is applied to understand and measure the difference in the distributions of two or more events. Events as you would appreciate are a discrete concept and translate to classes in the case of a ML classification problems. This is the reason that Cross Entropy is only applicable to Bernoulli/Multinoulli (categorical distributions).

In logistic regression, you assume that each target value follows a Bernoulli distribution - takes on value 1 with some probability $$p$$, and 0 with probability $$1-p$$. Your model predicts that the target takes on value 1 with some probability $$\hat{p}$$, and 0 with probability $$1-\hat{p}$$. You are in some sense comparing these two distributions, predicted and actual, by using log loss, yes.