Gaussian Processes (GPs) are sophisticated mathematical models known for their flexibility and ability to estimate uncertainty in machine learning. Their complexity, however, makes them challenging to grasp, particularly because most explanations heavily rely on advanced algebra and probability theory, making it hard to develop an intuitive understanding of their operation.
Intuition Over Mathematical Complexity
A plethora of guides exist that circumvent the mathematics to intuitively explain GPs, but such superficial understanding may not suffice in practice. A profound comprehension is essential when it comes to applying GPs appropriately. To facilitate this deeper insight, an explanation of a basic implementation from scratch, without relying on pre-built libraries, is provided to help users comprehend the intricacies involved.
Implementation and Practical Application
The provided GitHub repository contains the necessary code to implement GPs using only NumPy, with an aim to minimize but not entirely eliminate the mathematical complexity. The implementation uses a classic dataset from the Mauna Loa observatory, the same used by sklearn in their tutorial. This dataset records monthly atmospheric CO2 concentrations and is ideal for demonstrating the workings of GPs due to its simplicity and clear trends.
The dataset is particularly simple, consisting of a clearly observable upward linear trend and an annual seasonal cycle. Understanding these components is critical for explaining the subsequent mathematical concepts.
The approach involves isolating the seasonal and linear trends within the data. This is achieved by fitting a linear model, which serves as a preliminary step before delving into Gaussian Processes.
