I am currently studying Deep Learning by Goodfellow, Bengio, and Courville. In chapter 5.2 Capacity, Overfitting and Underfitting, the authors say the following:
Typically, when training a machine learning model, we have access to a training set; we can compute some error measure on the training set, called the training error; and we reduce this training error. So far, what we have described is simply an optimization problem. What separates machine learning from optimization is that we want the generalization error, also called the test error, to be low as well. The generalization error is defined as the expected value of the error on a new input. Here the expectation is taken across different possible inputs, drawn from the distribution of inputs we expect the system to encounter in practice.
I found this part unclear:
Here the expectation is taken across different possible inputs, drawn from the distribution of inputs we expect the system to encounter in practice.
The language used here is confusing me, because it is discussing a "distribution", as in a "probability distribution", but then refers to inputs, which are data gathered from outside of any probability distribution. Based on the limited information my studying of machine learning has taught me so far, my understanding is that the machine learning algorithm (or, rather, some machine learning algorithms) uses training data to implicitly construct some probability distribution, right? So is this what it is referring to here? Is the "distribution of inputs we expect the system to encounter in practice" the so called "test set"? I would greatly appreciate it if people would please take the time to clarify this.