Bayesian Network for Fare Classification

📚 Project Overview

This project focuses on developing a Bayesian network model for fare classification in a public transportation system. Using a dataset containing information about bus routes, stops, distances, and fare categories, we construct and evaluate three models:

1. An Initial Bayesian Network
2. A Pruned Bayesian Network
3. An Optimized Bayesian Network

Each model is tested on a validation dataset, and their performance is compared based on accuracy, runtime, and efficiency.

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🚀 Objective

• Build an initial Bayesian network for fare classification.
• Apply pruning techniques to simplify and enhance efficiency.
• Optimize the network using structure refinement methods.
• Compare the models based on accuracy, runtime, and efficiency.
• Return .pkl files for all three models.

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🧠 Dataset Features

The Bayesian network uses the following features:

• Start Stop ID (S): Stop ID where the journey begins.
• End Stop ID (E): Stop ID where the journey ends.
• Distance (D): Distance between start and end stops.
• Zones Crossed (Z): Number of fare zones crossed.
• Route Type (R): Type of route (e.g., standard, express).
• Fare Category (F): Target variable classified as Low, Medium, or High.

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🛠️ Tasks

Task 1: Initial Bayesian Network Construction

• Construct the Bayesian network using the specified features.
• Ensure dependencies between relevant feature pairs.
• Visualize the initial Bayesian network structure.
• Evaluate and record runtime and accuracy.

Task 2: Pruned Bayesian Network

• Apply pruning techniques:
  • Edge Pruning
  • Node Pruning
  • Conditional Probability Table (CPT) simplification
• Method Used: Independence Testing via bn.independence_test with prune=True. Edges failing the statistical significance test (alpha=0.05) are removed.
  • Independence tests use statistical methods like Chi-Square for categorical variables.
  • Strong evidence (p-value ≤ 0.05) indicates a meaningful connection; otherwise, edges are removed.
• Results:
  • Edge Reduction: 15 → 10 edges (33.33% reduction)
  • Fit Time Comparison:
    • Improvement: Approx. 12.2% reduction in fitting time
• Improvements:
  1. Efficiency: Reduced computational time and improved inference speed.
  2. Simplification: Statistically significant edges are retained, reducing overfitting risks.
  3. Potential Accuracy Improvement: The model is less likely to overfit, improving generalization.
• Visualize the pruned Bayesian network.

Task 3: Optimized Bayesian Network

• Apply optimization techniques such as Structure Learning (e.g., Hill Climbing).
• Method Used: Hill Climbing Algorithm with BIC (Bayesian Information Criterion) as the scoring metric.
  • Iteratively adds, removes, or reverses edges to minimize the BIC score.
• Results:
  • Edge Reduction: 15 → 4 edges (73.33% reduction)
  • Fit Time Comparison:
    • Improvement: Approx. 98.82% reduction in fitting time
• Improvements:
  1. Efficiency: Significant reduction in fitting and inference time.
  2. Simplification: A clearer structure focusing on the most important relationships.
  3. Generalization: Reduced overfitting risk and potential accuracy improvement.
• Visualize the optimized Bayesian network.

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📊 Evaluation Metrics

• Accuracy: Measure prediction correctness on the validation dataset.
• Runtime: Record time taken for initialization and training.
• Model Complexity: Analyze network structure and efficiency.

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📈 Results Visualization

• Graph Visualizations: Three Graphviz PNGs showing:
  1. Initial Bayesian Network
  2. Pruned Bayesian Network
  3. Optimized Bayesian Network
• Comparative analysis of accuracy, runtime, and efficiency.
• Observations and conclusions documented.

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⚙️ Setup and Usage

Virtual Environment Setup (Recommended)

To ensure a clean and isolated development environment, it is highly recommended to use a virtual environment (venv) for this project.

🛠️ Steps to Set Up venv:

1. Create a Virtual Environment:

   python -m venv venv

2. Activate the Virtual Environment:
   • On Windows:

   .\venv\Scripts\activate

   • On macOS/Linux:

   source venv/bin/activate

3. Install Dependencies:

   pip install -r requirements.txt

4. Deactivate the Environment (When Done):

   deactivate

5. Run the project:

   python FareClassification.py

6. Ensure .pkl files for each model are returned.

Note: By using venv, you can avoid dependency conflicts and maintain consistency across different development setups.

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📝 Conclusion

• Compared the efficiency and accuracy of the three Bayesian networks.
• Highlighted the impact of pruning and optimization on performance.
• Provided key insights into Bayesian network design for fare classification.

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📬 Contact

For questions or collaboration, feel free to reach out!

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Happy Coding! 🚀