Decision Tree Regression

Anh-Thi Dinh

What's the idea of Decision Tree Regression?

The basic intuition behind a decision tree is to map out all possible decision paths in the form of a tree. It can be used for classification (Decision Tree Classifier ) and regression. In this post, let's try to understand the regression.
DT Regression is similar to Decision Tree Classifier , however we use Mean Square Error (MSE, default) or Mean Absolute Error (MAE) instead of cross-entropy or Gini impurity to determine splits.
Suppose that we have a dataset like in the figure below,
An example of dataset .
A decision tree we want.

Some basic concepts

  • Splitting: It is a process of dividing a node into two or more sub-nodes.
  • Pruning: When we remove sub-nodes of a decision node, this process is called pruning.
  • Parent node and Child Node: A node, which is divided into sub-nodes is called parent node of sub-nodes where as sub-nodes are the child of parent node.
Other aspects of decision tree algorithm, check this note.
Looking for an example, read this file.
Below are a short algorithm:
  1. Calculate the Standard Deviation () of the current node (let's say , parent node) by using MSE or MAE,
    1. where the target values (Hours Played in the above example), is the mean value and is the number of examples in this node.
  1. Check the stopping conditions (we don't need to make any split at this node) to stop the split and this node becomes a leaf node. Otherwise, go to step 3.
      • The minimum number of samples required to split an internal node, use min_samples_split in scikit-learn.
      • The maximum depth of the tree, use max_depth in scikit-learn.
      • A node will be split if this split induces a decrease of the impurity greater than or equal to this value, use min_impurity_decrease in scikit-learn.
      • Its coefficient of variation () is less than a certain threshold.
  1. Calculate the Standard Deviation Reduction (SDR) after splitting node on each attribute (for example, consider attribute ). The attribute w.r.t. the biggest SDR will be chosen!
    1. where number of different properties in and is the propability of property in . Note that, means the SD of node which is also a child of node .
  1. After splitting, we have new child nodes. Each of them becomes a new parent node in the next step. Go back to step 1.

Using Decision Tree Regression with Scikit-learn

Load and create

Load the library,
1from sklearn.tree import DecisionTreeRegressor
Create a decision tree (other parameters):
1# mean squared error (default)
2reg = DecisionTreeRegressor() # criterion='mse'
3# mean absolute error
4reg = DecisionTreeRegressor(criterion='mae')
An example,
1from sklearn import tree
2X = [[0, 0], [2, 2]]
3y = [0.5, 2.5]
4reg = tree.DecisionTreeRegressor()
5reg =, y) # train
1# output

Plot and save plots

Plot the tree (You may need to install Graphviz first. Don't forget to add its installed folder to $path),
1from IPython.display import Image
2import pydotplus
3dot_data = tree.export_graphviz(reg, out_file=None,
4                                rounded=True,
5                                filled=True)
6graph = pydotplus.graph_from_dot_data(dot_data)
Save the tree (follows the codes in "plot the tree")
1graph.write_pdf("tree.pdf")   # to pdf
2graph.write_png("thi.png")    # to png