Introduction and Motivation 1.1 Finding Words for Intuitions Machine learning is about designing algorithms that learn from data. The goal is to find good models that generalize well to future data. The challenge is that the concepts and words are slippery, and a particular component of the machine learning system can be abstracted to different mathematical concepts. For example, the word “algorithm” is used in at least two different senses in the context of machine learning. In the first sense, we use the phrase “machine learning algorithm” to mean a system that makes predictions based on input data. We refer to these algorithms as predictors. In the second sense, we use the exact same phrase “machine learning algorithm” to mean a system that adapts some internal parameters of the predictor so that it performs well on future unseen input data. Here we refer to this adaptation as training a predictor. The first part of this book describes the mathematical concepts and foundations needed to talk about the three main components of a machine learning system: data, models, and learning. We will briefly outline these components here, and we will revisit them again in Chapter 8 once we have the mathematical language under our belt. Adding to the challenge is the fact that the same English word could mean different mathematical concepts, and we can only work out the precise meaning via the context. We already remarked about the overloaded use of the word “algorithm”, and the reader will be faced with other such phrases. We advise the reader to use the idea of “type checking” from computer science and apply it to machine learning concepts. Type checking allows the reader to sanity check whether the equation that they are considering contains inputs and outputs of the correct type, and whether they are mixing different types of object