Logistic regression as a neural network

As a teacher of Data Science (Data Science for Internet of Things course at the University of Oxford), I am always fascinated in cross connection between concepts. To recap, Logistic regression is a binary classification method. It can be modelled as a function that can take in any number of inputs and constrain the output to be between 0 and 1. This means, we can think of Logistic Regression as a one-layer neural network. For a binary output, if the true label is y (y 0 or y 1) and y_hat is the predicted output – then y_hat represents the probability that y 1 - given inputs w and x. Therefore, the probability that y 0 given inputs w and x is (1 - y_hat), as shown below.