How do leaf nodes behave in regression decision trees?

In summary, leaf nodes in regression decision trees represent the final output for predictions, where each leaf corresponds to a specific value or average of the target variable based on the samples that reach that node. They aggregate the outcomes of the input features processed through the tree's decision-making structure, allowing for continuous value predictions. The behavior of leaf nodes is crucial as they determine the model's accuracy and generalization by capturing the underlying trends in the data.
  • #1
fog37
1,569
108
TL;DR Summary
understand how decision trees and leaf nodes behave in the case of regression...
Hello.

Decision trees are really cool. They can be used for either regression or classification. They are built with nodes and each node represents an if-then statement that gets evaluated to be either true or false. Does that mean there are always and only two edges/branches coming out of an internal node (leaf nodes don't have edges)? Or are there situations in which there can be more than 2 edges?

In the case of classification trees, the leaf nodes are the output nodes, each with a single class output (there can be more leaf nodes than the classes available). In the case of regression trees, how do the leaf nodes behave? The goal is to predict a numerical output (ex: the price of a house). How many leaf nodes are there? One for each possible numerical value? That would be impossible. I know the tree gets trained with a finite number of examples/instances and the tree structure and decision statements are formed...

Thank you for any clarification.
 
Physics news on Phys.org
  • #2
I have never heard of using a decision tree for regression. Do you have a source for this?
 
  • #4
fog37 said:
TL;DR Summary: understand how decision trees and leaf nodes behave in the case of regression...

In the case of regression trees, how do the leaf nodes behave? The goal is to predict a numerical output (ex: the price of a house). How many leaf nodes are there? One for each possible numerical value?
It looks like the leaves themselves can assume continuous outputs. So you would only need one leaf per regression parameter.
 
  • Like
Likes fog37
  • #5
Dale said:
It looks like the leaves themselves can assume continuous outputs. So you would only need one leaf per regression parameter.
Thank you. Let me see if I understand correctly. In the example figure below, I notice that the leaf nodes have specific amounts, i.e. the value (last line). What if the inputs are such that the predicted value is none of the values mentioned in the leaf nodes? That is my dilemma. It seems that there is a finite number of leaf nodes having their own value...

1699537077116.png
 
  • #6
Sorry, I cannot help you. Literally all I know about it is that one page that you cited where it says "Continuous output means that the output/result is not discrete, i.e., it is not represented just by a discrete, known set of numbers or values".

If you need more technical information then you need to find a more technical source. If you have a more technical source that has the information you need then I can help you understand it, but there simply is not any more information available there than the quote.
 
  • Like
Likes fog37
  • #7
Dale said:
Sorry, I cannot help you. Literally all I know about it is that one page that you cited where it says "Continuous output means that the output/result is not discrete, i.e., it is not represented just by a discrete, known set of numbers or values".

If you need more technical information then you need to find a more technical source. If you have a more technical source that has the information you need then I can help you understand it, but there simply is not any more information available there than the quote.
No worries.

After some research, I learned that, in the case of a regression decision tree, the possible numerical output answers are the averages of the values for those instances in the training dataset that together reached a particular leaf node based on the sequence of if-then statements along the tree itself...
 
  • Like
Likes Dale

FAQ: How do leaf nodes behave in regression decision trees?

What is the role of leaf nodes in regression decision trees?

Leaf nodes in regression decision trees represent the final output or prediction of the model. They contain the predicted value for the target variable, which is typically the mean or median of the target values of the data points that fall into that node.

How are the values in leaf nodes determined?

The values in leaf nodes are determined by aggregating the target values of all the data points that reach that node. Common aggregation methods include calculating the mean or median of these target values, which serves as the predicted value for any new data point that falls into this leaf node.

What happens if a leaf node has very few data points?

If a leaf node has very few data points, it can lead to overfitting, where the model becomes too tailored to the specific data points in that node and loses generalizability. To mitigate this, techniques such as pruning or setting a minimum number of data points per leaf node are used.

Can leaf nodes handle missing values in the data?

Handling missing values in leaf nodes depends on the implementation of the regression decision tree algorithm. Some algorithms can handle missing values by assigning them to the most frequent or mean value of the feature, or by using surrogate splits to find the best alternative way to split the data when missing values are encountered.

How do leaf nodes affect the interpretability of regression decision trees?

Leaf nodes contribute to the interpretability of regression decision trees by providing clear and specific predictions based on the input features. Each path from the root to a leaf node represents a set of conditions that lead to a particular prediction, making it easier to understand how the model makes decisions.

Similar threads

MHB Propositional Logic - Derivations and Trees - Chiswell and Hodges, Section 3.4
Replies
1
Views
2K
Proving the Number of Leaves is One More Than Internal Nodes in Binary Trees
Replies
1
Views
2K
I Is it better to use a regression or a classification?
Replies
13
Views
2K
Algorithm for computing the depths of all the nodes of tree
Replies
1
Views
2K
MHB Binary Search Tree - Sort the same BSTree by name or by weight
Replies
3
Views
2K
M-ary Tree: Given Nodes, find leaves
Replies
9
Views
3K
Finding a Local Minimum in a Complete Binary Tree with Log(N) Probes
Replies
1
Views
2K
Minimizing height of binary search tree
Replies
1
Views
3K
Rooted tree impossible constructs
Replies
1
Views
1K
Python Create a binary search tree in python with the support of variables
Replies
13
Views
4K

Hot Threads

Recent Insights

Back
Top