A Visual Exploration of Gaussian Processes (2019)

Summary

Even if you have spent some time reading about machine learning, chances are that you have never heard of Gaussian processes. And if you have, rehearsing the basics is always a good way to refresh your memory. With this blog post we want to give an introduction to Gaussian processes and make the mathematical intuition behind them more approachable. Gaussian processes are a powerful tool in the machine learning toolbox. They allow us to make predictions about our data by incorporating prior knowledge. Their most obvious area of application is fitting a function to the data. This is called regression and is used, for example, in robotics or time series forecasting. But Gaussian processes are not limited to regression — they can also be extended to classification and clustering tasks. For a given set of training points, there are potentially infinitely many functions that fit the data. Gaussian processes offer an elegant solution to this problem by assigning a probability to each of these functions. The mean of this probability distribution then represents the most probable characterization of the data. Furthermore, using a probabilistic approach allows us to incorporate the confidence of the prediction into the regression result. We will first explore the mathematical foundation that Gaussian processes are built on — we invite you to follow along using the interactive figures and hands-on examples. They help to explain the impact of individual components, and show the flexibility of Gaussian processes. After following this article we hope that you will have a visual intuition on how Gaussian processes work and how you can configure them for different types of data. Multivariate Gaussian distributions Before we can explore Gaussian processes, we need to understand the mathematical concepts they are based on. As the name suggests, the Gaussian distribution (which is often also referred to as normal distribution) is the basic building block of Gaussian processes. In part...