Every machine learning model really starts with a cost function. Simply, a cost function allows you to measure how well your model is fitting the training data. In this book, we will define the loss function as the correctness of fit for a single observation within the training set. The cost function will then most often be an average of the loss across the training set. We will revisit loss functions later when we introduce each type of neural network; however, quickly consider the cost function for linear regression as an example:

In this case, the loss function would be , which is really the squared error. So then J, our cost function, is really just the mean squared error, or an average of the squared error across the entire dataset. The term 1/2 is added to make some of the calculus cleaner by convention.