Understanding binary cross-entropy / log loss: a visual explanation

If you are training a binary classifier, chances are you are using binary cross-entropy / log loss as your loss function. Have you ever thought about what exactly does it mean to use this loss function? The thing is, given the ease of use of today's libraries and frameworks, it is very easy to overlook the true meaning of the loss function used. I was looking for a blog post that would explain the concepts behind binary cross-entropy / log loss in a visually clear and concise manner, so I could show it to my students at Data Science Retreat. Let's start with 10 random points: This is our only feature: x.