Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction

Abstract: For large, real-world inductive learning problems, the number of training examples often must be limited due to the costs associated with procuring, preparing, and storing the training examples and/or the computational costs associated with learning from them. In such circumstances, one question of practical importance is: if only n training examples can be selected, in what proportion should the classes be represented? In this article we help to answer this question by analyzing, for a fixed training-set size, the relationship between the class distribution of the training data and the performance of classification trees induced from these data. We study twenty-six data sets and, for each, determine the best class distribution for learning. The naturally occurring class distribution is shown to generally perform well when classifier performance is evaluated using undifferentiated error rate (0/1 loss). However, when the area under the ROC curve is used to evaluate classifier performance, a balanced distribution is shown to perform well. Since neither of these choices for class distribution always generates the best-performing classifier, we introduce a budget-sensitive progressive sampling algorithm for selecting training examples based on the class associated with each example. An empirical analysis of this algorithm shows that the class distribution of the resulting training set yields classifiers with good (nearly-optimal) classification performance.

• The paper presents a cost-sensitive method that selects the optimal class distribution for decision tree induction with limited training data.
• It empirically evaluates 26 UCI datasets to measure error rate and AUC variations across different class distributions.
• The study introduces a progressive sampling algorithm that efficiently balances training costs with improved classifier accuracy.

Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction

The paper "Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction," authored by Gary M. Weiss and Foster Provost and published in the Journal of Artificial Intelligence Research (JAIR) in 2003, examines the pivotal role of class distribution in constructing classification trees under constraints of limited training data. This research is especially impactful for settings where acquiring training data incurs significant costs.

Core Contributions

The paper makes two principal contributions:

1. It addresses the practical issue of determining the optimal class distribution for a fixed training set size in classification-tree induction.
2. It presents an empirical analysis revealing how class distribution affects classifier performance, and introduces a progressive sampling algorithm to mitigate class distribution effects while being cost-sensitive.

Empirical Methodology

The researchers provide a detailed empirical study utilizing 26 data sets, primarily sourced from the UCI repository, examining the relationship between class distribution and performance metrics such as undifferentiated error rate and area under the ROC curve (AUC). The study comprehensively outlines the methodology for generating training and test sets, ensuring consistency in training set size across various class distributions.

Findings and Analysis

Error Rate and AUC Analysis

The study articulates two distinct findings based on the metrics used:

• Error Rate: The naturally occurring class distribution generally shows good performance. However, the analysis reveals that for highly imbalanced data sets, a balanced distribution does not always guarantee optimal performance.
• AUC: A balanced class distribution often yields high AUC values, indicating superior classifier performance for a range of class distributions.

Impact of Class Distribution

The experiments underline that altering the class distribution of the training set significantly impacts classifier performance. For instance, the corrected frequency-based estimate method shows an average relative reduction in error rate of 10.6% over the uncorrected method, highlighting the importance of adjusting class distributions.

Budget-Sensitive Progressive Sampling Algorithm

To address the issue of costly training data, Weiss and Provost propose a "budget-sensitive" progressive sampling algorithm. This method incrementally selects training examples, adjusting the class distribution based on empirical performance evaluations. The algorithm is budget-efficient, ensuring that all requested examples are utilized in the final training set, thereby balancing cost and classifier performance optimally.

Implications and Future Work

Practical Implications

The findings underscore the need for practitioners to carefully consider class distribution when training data are costly. The progressive sampling algorithm offers a pragmatic solution by dynamically adjusting the class distribution, minimizing data procurement costs while maintaining classifier performance.

Theoretical Implications

The theoretical implications extend to improving the understanding of class distribution's role in learning. The study suggests that class distribution greatly influences the performance of classifiers, particularly for domains where data imbalance is prevalent (e.g., fraud detection, medical diagnosis).

Future Research Directions

Future explorations could expand this research by:

1. Extending the analysis to other types of learners beyond decision trees (e.g., support vector machines, neural networks), potentially yielding broader applicability of the findings.
2. Developing pruning strategies that account for distribution changes and cost considerations, potentially further enhancing classifier performance.
3. Investigating non-uniform data procurement costs, which could refine the sampling algorithm for more complex real-world scenarios where data labels come at different costs.

Conclusion

The paper by Weiss and Provost is a seminal contribution towards understanding and improving classifier performance when training data are scarce and costly. By providing empirical evidence and proposing a practical algorithm, the research offers valuable guidelines for data procurement and model training in real-world applications.

The research fundamentally advises against arbitrary class distribution choices, advocating for data-driven, budget-conscious decisions to enhance machine learning results in cost-sensitive domains. This work remains a critical reference point for enhancing learning algorithms' efficiency under economic constraints.