Effective Strategies for Cost-Sensitive Decision Trees in Data Science
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Chapter 1: Understanding Cost-Sensitive Decision Trees
This article explores the application of decision trees as a cost-sensitive supervised learning algorithm, particularly in the context of imbalanced datasets.
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Decision trees are widely utilized for classification and regression tasks. The classification variant employs a tree-like structure to categorize instances. One of the significant advantages of decision trees is their clarity and interpretability.
The structure is composed of a single root node, multiple internal nodes, and several leaf nodes. Leaf nodes deliver outcomes, while internal nodes serve as tests for feature values. Instances within a node are allocated to child nodes based on these feature tests. The root node encompasses all instances, meaning that every path from the root to a leaf represents a sequence of tests. The objective is to construct a decision tree with strong generalization capabilities to handle previously unseen instances.
Loss Function in Decision Trees
The loss function for a decision tree is based on a maximum likelihood function that incorporates regularization. Finding the optimal tree among all potential trees is a non-deterministic polynomial-time (NP) problem. As a result, heuristic methods are typically employed to find a sub-optimal solution. The construction of a decision tree is achieved through a divide-and-conquer strategy, outlined as follows:
A crucial step in this process is Step 8: selecting the optimal feature to develop new branches. The guiding principle for this selection is to ensure that instances in the child node belong to the same class as much as possible, resulting in high "purity." Two common measures of impurity are Entropy and Gini.
If the target represents a classification outcome that can take on values 1, 2, …, K from set D:
The entropy of D is defined as follows:
The Gini index for D is given by:
Assuming D can be divided into left and right child nodes based on feature a, with N(left) indicating the number of instances in the left child node and N(right) for the right child node:
A lower value for child nodes indicates that feature a results in higher purity. Thus, the goal is to select a feature that minimizes G(D, a):
Decision Trees in Imbalanced Datasets
In scenarios with imbalanced data, class weights vary. These class weights can be converted into instance weights. It is evident that outlier instances should have higher weights, while inlier instances should have lower weights.
Consequently, P(k) can be computed as:
Ultimately, G in the context of imbalanced settings can be calculated as:
Conclusion
There are several approaches for handling imbalanced data using supervised methods, including undersampling, oversampling, and cost-sensitive learning. Undersampling involves removing samples from the majority class, while oversampling entails generating new samples from the minority class. Cost-sensitive learning assigns a higher cost to misclassifications of minority class samples compared to those of majority class samples.
This article has highlighted the role of decision trees in addressing imbalanced data through cost-sensitive learning techniques.
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