Astronomy is a data-driven science in which relationships between physical quantities are inferred and validated through observation. Classical examples include the relationships between stellar mass, temperature, radius, and luminosity. In this homework, you will implement linear regression and polynomial regression from first principles, without using machine-learning libraries.
Rather than calling pre-built fitting routines, you will explicitly define the hypothesis function, the loss function, and the optimization algorithm. The astronomical problem studied here is a simplified stellar luminosity modeling task, inspired by main-sequence behavior: luminosity grows rapidly with mass, and additional properties can introduce nonlinear and interaction effects.
This homework is part of a four-week Machine Learning Bootcamp embedded in a course on Digital Transformation and Enterprise Architecture. In this context, machine learning is treated as a core architectural capability of modern enterprise systems.
Today, intelligence is increasingly considered a first-class quality attribute alongside scalability, availability, security, and performance. Intelligent behavior is no longer confined to offline analytics; it is embedded into platforms, decision-support services, and autonomous or semi-autonomous components.
As enterprise architects, it is not sufficient to understand what models do. We must also understand how they are built from first principles, executed and validated in controlled environments, and operated within cloud platforms.
- Deliver all work in a single GitHub repository.
- The repository must contain two Jupyter notebooks and one README.md.
- All code must be written inside the notebooks.
- All datasets must be defined directly in the notebooks (as hard-coded NumPy arrays).
- Allowed libraries: Python, NumPy, Matplotlib (inline plots only).
- Not allowed: scikit-learn, statsmodels, TensorFlow/PyTorch, or any high-level regression/optimization library.
/
├── README.md
├── 01_part1_linreg_1feature.ipynb
└── 02_part2_polyreg.ipynb
Use the following notation throughout:
- M: stellar mass (in units of solar mass, M⊙)
- T: effective stellar temperature (Kelvin, K)
- L: stellar luminosity (in units of solar luminosity, L⊙)
M = [0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4]
L = [0.15, 0.35, 1.00, 2.30, 4.10, 7.00, 11.2, 17.5, 25.0, 35.0]M = [0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4]
T = [3800, 4400, 5800, 6400, 6900, 7400, 7900, 8300, 8800, 9200]
L = [0.15, 0.35, 1.00, 2.30, 4.10, 7.00, 11.2, 17.5, 25.0, 35.0]Notebook: 01_part1_linreg_1feature.ipynb
Notebook: 02_part2_polyreg.ipynb
- Python 3.7+
- NumPy (numerical computations)
- Matplotlib (visualization)
- scikit-learn
- statsmodels
- TensorFlow/PyTorch
- Any high-level regression/optimization library
This project emphasizes first-principles understanding:
- Build gradient descent from scratch
- Implement analytical gradient computation
- Understand convex optimization
- Diagnose model failures through residuals
- Compare vectorized vs loop-based implementations
In modern enterprise systems, intelligence is a first-class architectural quality alongside:
- Scalability: Handle growing data and requests
- Availability: Ensure uptime and reliability
- Security: Protect data and models
- Performance: Optimize latency and throughput
- Intelligence: Embed ML for decision-support
- Reproducibility: Jupyter notebooks in containers ensure consistent environments
- Scalability: Train on larger datasets with cloud compute
- Collaboration: Share notebooks via GitHub for peer review
- Deployment: Package models as microservices (MLOps)
- Monitoring: Track model performance in production
David Stiven Sarria Arcila
Machine Learning Bootcamp
Digital Transformation and Enterprise Architecture Course
January 2026