#### Overview of this book

Machine Learning for Finance explores new advances in machine learning and shows how they can be applied across the financial sector, including insurance, transactions, and lending. This book explains the concepts and algorithms behind the main machine learning techniques and provides example Python code for implementing the models yourself. The book is based on Jannes Klaas’ experience of running machine learning training courses for financial professionals. Rather than providing ready-made financial algorithms, the book focuses on advanced machine learning concepts and ideas that can be applied in a wide variety of ways. The book systematically explains how machine learning works on structured data, text, images, and time series. You'll cover generative adversarial learning, reinforcement learning, debugging, and launching machine learning products. Later chapters will discuss how to fight bias in machine learning. The book ends with an exploration of Bayesian inference and probabilistic programming.
Machine Learning for Finance
Contributors
Preface
Other Books You May Enjoy
Free Chapter
Applying Machine Learning to Structured Data
Utilizing Computer Vision
Understanding Time Series
Parsing Textual Data with Natural Language Processing
Using Generative Models
Reinforcement Learning for Financial Markets
Privacy, Debugging, and Launching Your Products
Fighting Bias
Bayesian Inference and Probabilistic Programming
Index

## Approximating functions

There are many views on how best to think about neural networks, but perhaps the most useful is to see them as function approximators. Functions in math relate some input, x, to some output, y. We can write it as the following formula:

A simple function could be like this:

In this case, we can give the function an input, x, and it would quadruple it:

You might have seen functions like this in school, but functions can do more; as an example, they can map an element from a set (the collection of values the function accepts) to another element of a set. These sets can be something other than simple numbers.

A function could, for example, also map an image to an identification of what is in the image:

This function would map an image of a cat to the label "cat," as we can see in the following diagram:

Mapping images to labels

We should note that for a computer, images are matrices full of numbers and any description of an image's content would also be stored as a matrix of numbers.

A neural network, if it is big enough, can approximate any function. It has been mathematically proven that an indefinitely large network could approximate every function. While we don't need to use an indefinitely large network, we are certainly using very large networks.

Modern deep learning architectures can have tens or even hundreds of layers and millions of parameters, so only storing the model already takes up a few gigabytes. This means that a neural network, if it's big enough, could also approximate our function, f, for mapping images to their content.

The condition that the neural network has to be "big enough" explains why deep (big) neural networks have taken off. The fact that "big enough" neural networks can approximate any function means that they are useful for a large number of tasks.