Estimating the Accuracy of a Bagged Ensemble

Abstract

This paper presents a novel probabilistic framework for estimating the accuracy of bagged ensemble models, specifically Random Forests, without exhaustive computational evaluation. Our approach uses various probability distributions to model ensemble performance, achieving less than 3% relative error across varying configurations while significantly reducing computational overhead.

Introduction

Model fine-tuning and hyperparameter optimization for ensemble methods typically require extensive computational resources. This research addresses the challenge of efficiently estimating ensemble performance without complete evaluation.

Methodology

Probabilistic Framework

We developed a mathematical framework that models Random Forest accuracy using probability distributions. The key components include:

1. Distribution Selection: Testing various probability distributions to model accuracy
2. Parameter Estimation: Efficient methods for distribution parameter fitting
3. Validation: Cross-validation across different Random Forest configurations

Experimental Setup

• Datasets: Multiple benchmark datasets with varying characteristics
• Forest Configurations: Different numbers of trees, max depth, and other hyperparameters
• Evaluation Metrics: Relative error, computational time savings

Key Results

• Accuracy: Less than 3% relative error in accuracy estimation
• Efficiency: Significant reduction in computational overhead
• Robustness: Consistent performance across different configurations
• Generalization: Framework applicable to various bagging-based ensembles

Theoretical Contributions

The research provides:

• Mathematical formulation of ensemble accuracy estimation
• Proof of error bounds
• Computational complexity analysis

Practical Applications

This framework enables:

• Faster hyperparameter tuning
• Efficient AutoML pipelines
• Resource-constrained model development

Implementation

The methodology was implemented in Python using scikit-learn for Random Forest models and statistical libraries for distribution fitting.

Conclusion

Our probabilistic approach to estimating bagged ensemble accuracy offers a practical solution for reducing computational costs in model development while maintaining high accuracy in performance prediction.

Publication Details

Published in: Machine Learning and Applications: An International Journal (MLAIJ)
DOI: 10.5121/mlaij.2025.12106
Authors: Shah, S., & Pinsky, E.