Essential Math for AI

Chapter 3. Fitting Functions to Data

Today it fits. Tomorrow?

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In this chapter, we introduce the core mathematical ideas lying at the heart of many AI applications, including the mathematical engines of neural networks. Our goal is to internalize the following structure of the machine learning part of an AI problem:

Identify the problem

The problem depends on the specific use case: classify images, classify documents, predict house prices, detect fraud or anomalies, recommend the next product, predict the likelihood of a criminal reoffending, predict the internal structure of a building given external images, convert speech to text, generate audio, generate images, generate video, etc.

Acquire the appropriate data

This is about training our models to do the right thing. We say that our models learn from the data. Make sure this data is clean, complete, and if necessary, depending on the specific model we are implementing, transformed (normalized, standardized, some features aggregated, etc.). This step is usually way more time-consuming than implementing and training the machine learning models.

Create a hypothesis function

We use the terms hypothesis function, learning function, prediction function, training function, and model interchangeably. Our main assumption is that this input/output mathematical function explains the observed data, and it can be used later to make predictions on new data. We give our model features, like a person’s daily habits, and it returns ...