In this chapter, we will be working in Python 3 with the scikit-learn scientific computing package. You can install the package, you can run pip install sklearn in your terminal or command line.

When we talk about mathematics as related to deep learning and AI, we're often talking about linear algebra. Linear algebra is a branch of continuous mathematics that involves the study of vector space and operations performed in vector space. If you remember back to grade-school algebra, algebra in general deals with unknown variables. With linear algebra, we're extending this study into linear systems that have an arbitrary number of dimensions, which is what makes this a form of continuous mathematics.

AI relies on the basic building block of the tensor. Within AI, these mathematical objects store information throughout ANNs that allow them to operate; they are data structures that are utilized throughout AI. As we will see, a tensor has a rank, which essentially tells us about the indices of the data (how many rows and columns the data has).

Probability, the mathematical method for modeling uncertain scenarios, underpins the algorithms that make AI intelligent, helping to tell us how our systems should reason. So, what is probability? We'll define it as follows:

Simply said, probability is the mathematical study of uncertainty. In this section, we'll cover the basics of probability space and probability distributions, as well as helpful tools for solving simple problems.

When probability is discussed, it's often referred to in terms of the probability of a certain event happening. Is it going...

As mentioned in the last chapter, machine learning is a term that was developed as a reaction to the first AI winter. Today, we generally consider machine learning to be the overarching subject area for deep learning and ANNs in general.

Most machine learning solutions can be broken down into either a classification problem or a regression problem. A classification problem is when the output variables are categorical, such as fraud or not fraud. A regression problem is when the output is continuous, such as dollars or site visits. Problems with numerical output can be categorical, but are typically transformed to have a categorical output such as first class and second class.

Within machine learning, we have supervised algorithms and unsupervised algorithms. In this section, we will introduce these types of algorithms and explore...

So you've built a model, now what? Can you call it a day? Chances are, you'll have some optimization to do on your model. A key part of the machine learning process is the optimization of our algorithms and methods. In this section, we'll be covering the basic concepts of optimization, and will be continuing our learning of tuning methods throughout the following chapters.

Sometimes, when our models do not perform well with new data it can be related to them overfitting or underfitting. Let's cover some methods that we can use to prevent this from happening. First off, let's look at the random forest classifier that we trained earlier. In your notebook, call the predict method on it and pass the x_test data in to receive some predictions:

predicted = rf_classifier.predict(x_test)

From this, we can create evaluate the performance of our classifier...

Machine learning, and by extension, deep learning, relies on the building blocks of linear algebra and statistics at its core. Vectors, matrices, and tensors provide the means by which we represent input data and parameters in machine learning algorithms, and the computations between these are the core operations of these algorithms. Likewise, distributions and probabilities help us model data and events in machine learning.

We also covered two classes of algorithms that will inform how we think about ANNs in further chapters: supervised learning methods and unsupervised learning methods. With supervised learning, we provide the algorithm with a set of features and labels, and it learns how to appropriately map certain feature combinations to labels. In unsupervised learning, the algorithm isn't provided with any labels at all, and it must infer relationships and...