Before we venture into what will likely be the most challenging section of this book for many readers, I think it’s important to clarify a crucial point. By now, after so many introductions, it should be clear that machine learning algorithms are a powerful machine built on as much data as possible (preferably Big Data). Data, are “given”, meaning they are known quantities! And it’s essential not to confuse them with solutions! The solutions, on the other hand, are unknowns, and they must be found. Every time we face a mathematical problem, the challenge is to go from data to solutions, i.e., from input to output. How to do that is what we are discussing in this book. We can think of machine learning as a process that allows us to associate a certain set of data with the corresponding solution. Whether it’s assigning a label that indicates whether a particular photo shows a dog or something else, or recognizing whether a certain medical image (such as a CT scan or MRI) hides the presence of a tumor, and if so, which type of tumor it is, or partitioning a set of individuals into subsets with similar characteristics (such as their spending capacity or tendency to develop specific diseases), or even forecasting the weather for the upcoming weekend based on current data like wind speed, atmospheric pressure, and humidity. As can be guessed from these examples, the types of data can vary greatly, and the solutions that can be associated with them will also be very different. What remains unchanged is the mathematical structure: the trinomial: data → mathematical procedure → solutions.