Machine Learning the Spectrum of X-ray Binaries

Predicting $\log(N_H)$ and $\Gamma$ from X-ray Colours using Machine Learning

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📘 What is this repository?

This repository contains the full code and analysis accompanying the project Machine Learning the Spectrum of X-ray Binaries. The goal of the study is to explore whether X-ray colours, derived from Chandra X-ray Observatory data, can be used to infer two key spectral parameters:

• $\log(N_H)$: Logarithm of the hydrogen column density
• $\Gamma$: Photon index describing the slope of the intrinsic X-ray spectrum

We evaluate three machine learning regressors—Polynomial Regression, K-Nearest Neighbors (KNN), and Random Forest Regression (RFR)—to learn this mapping from colour space to physical parameters.

📝 You can read the full report here.

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📜 License

This project is licensed under the MIT License - see the LICENSE file for details.

When using this code, please:

• Retain the original license/copyright notice.
• Attribute by linking back to this repository (e.g., Machine Learning the Spectrum of X-ray Binaries by Elizabeth Birch Hardwick).

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📁 Repository structure

📄 main.ipynb                         # Main Jupyter Notebook
📄 LICENSE                            # MIT License file
📄 points_results_cycle3.csv          # Data used to train model (Cycle 3)
📄 points_results_current_cycle.csv   # Data used to train model (Cycle 25)
📄 train3.csv                         # Train data for train-test split used in article (Cycle 3)
📄 test3.csv                          # Test data for train-test split used in article (Cycle 3)
📄 train25.csv                        # Train data for train-test split used in article (Cycle 25)
📄 test25.csv                         # Test data for train-test split used in article (Cycle 25)
📄 poly_coefficients_cycle3.csv       # Exported polynomial regression coefficients (Cycle 3)
📄 poly_coefficients_cycle25.csv      # Exported polynomial regression coefficients (Cycle 25)
📄 use_coefficients_example.ipynb     # Notebook demonstrating how to use exported coefficients
📄 README.md                          # This file

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📓 Usage

Open the main notebook:

git clone https://github.com/elizabethbirchhardwick/Machine_Learning_the_Spectrum_of_X-ray-Binaries.git
cd Machine_Learning_the_Spectrum_of_X-ray-Binaries
pip install -r requirements.txt
jupyter notebook main.ipynb

Inside the notebook, you'll find:

• 📊 Data generation and visualization
• 🤖 Training and cross-validating three ML models
• 🔁 Cycle comparison (Cycle 3 vs Cycle 25)
• 🧽 Error filtering by removing high-uncertainty regions
• 📈 Visual evaluation using scatter and MAE contour plots
• 🧮 Model interpretation and coefficient export

All output cells are pre-run for convenience, but feel free to rerun and experiment!

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📤 Using the Polynomial Coefficients CSV

We trained polynomial regression models on both Cycle 3 and Cycle 25 datasets. The learned coefficients and bias terms for each were exported to CSV files:

• poly_coefficients_cycle3.csv
• poly_coefficients_cycle25.csv

These files allow you to reconstruct predictions for $\log(N_H)$ and $\Gamma$ manually or in other programming environments:

1. Import new values of H and S (hard and soft colours).
2. Use the same polynomial expansion (same degree) as in the notebook.
3. Apply the formula $\text{prediction} = \text{bias} + \sum_{i=1}^n \text{coef}_i \cdot \text{feature}_i$

To simplify this process, we also include a helper notebook:

jupyter notebook use_coefficients_example.ipynb

This notebook demonstrates how to load the CSV files and use them to compute predictions step by step.

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💬 Support

For questions or suggestions, feel free to reach out:

📧 elizabethbirchhardwick@gmail.com
🚀 Or open an issue on GitHub