Hands-On Machine Learning for Algorithmic Trading

How to build a regression tree

Regression trees make predictions based on the mean outcome value for the training samples assigned to a given node and typically rely on the mean-squared error to select optimal rules during recursive binary splitting.

Given a training set, the algorithm iterates over the predictors, X₁, X₂, ..., X_p, and possible cutpoints, s₁, s₁, ..., s_N, to find an optimal combination. The optimal rule splits the feature space into two regions, {X|X_i < s_j} and {X|X_i > s_j}, with values for the X_i feature either below or above the s_j threshold so that predictions based on the training subsets maximize the reduction of the squared residuals relative to the current node.

Let's start with a simplified example to facilitate visualization ...