PyGLMs (Turtles) 🐢

An implementation of various Generalized Linear Models (GLMs), written in Python.

I created this package as a refresher on GLMs and the underlying optimization techniques. It's intended as a learning tool and a reference for building and understanding these models from the ground up.

Overview

The code is packaged as a Python library named turtles (I like turtles), making the code easy to integrate into your own projects.

The package is written using numpy for linear algebra operations, scipy for (some) optimization, pandas for displaying tabular results, and matplotlib for plots.

The following models have been implemented:

1. Multiple Linear Regression (turtles.stats.glms.MLR class)
2. Logistic Regression (turtles.stats.glms.LogReg class, uses GLM parent class)
3. Poisson Regression (turtles.stats.glms.PoissonReg class, uses GLM parent class)

The GLM parent class supports three optimization methods for parameter estimation: Momentum-based Gradient Descent for first-order optimization, Newton's Method for second-order optimization, and Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS). The user can specify the desired optimization method during class instantiation.

Momentum-based Gradient Descent and Newton's Method are implemented in Python as part of the turtles distribution. L-BFGS is implemented using scipy.optimize; it's a quasi-Newton method that approximates the Hessian (instead of fully computing it, like Newton's Method), so it's quite fast.

Usage

You can pip install the package from PyPI:

pip install turtles-glms

See examples/ in the GitHub repo for example usage of the GLM classes and statistical functions.

Fitting GLMs

You can fit GLMs by instantiating a GLM class and calling its fit() method.

model = PoissonReg(
    method="newton",
    learning_rate=0.01
)
n_model.fit(
    X=X, 
    y=y, 
    exposure=exposure
)

A few important notes about fitting turtles GLMs:

1. The fit() method parameters X, y, and (for Poisson) exposure must be numpy arrays. Parameters y and exposure must be of shape (M, 1), where M is the number of rows in the data. The package does not support pandas or polars dataframes at this time. See class / instance method docstrings for exact requirements.
2. Each GLM class has a learning_rate parameter, applicable to Gradient Descent and Newton's optimization methods. The learning rate (or step size) is a hyperparameter that controls the magnitude of parameter updates during the optimization process. If it's too large, the Hessian matrix may become singular, in which case the learning rate should be decreased. This is typically part of the tuning process.
3. There are currently no regularization methods implemented in the package. Future versions may include L1, L2, and Elastic Net methods.

Contributing

To run (and edit) this project locally, clone the repo and create your virtual environment from project root using your global (or local) Python version. This project requires Python 3.10+.

python -m venv

Activate the env (source .venv/Scripts/activate for Windows OS, source .venv/bin/activate for Linux) and install dependencies:

pip install -e .[dev]

Optionally, you can execute scripts/env.sh to create and activate a virtual environment using uv. The uv package manager must be installed for this to work.

Adding GLMs

To add more GLM classes, use the GLM parent class for inheritence (see PoissonReg and LogReg as examples). The GLM parent class provides a solid framework for implementing new child classes and should be used whenever possible. Unimplemented GLMs include Negative Binomial, Gamma, and Tweedie.

Testing

All tests are contained within tests directories for each module. You can simply execute the pytest command from project root to run all unit tests.

pytest

Notes on Test Coverage:

• Plotting functions from turtles.plotting are tested, but plotting methods in GLM classes (like MLR) are ignored. Those class methods are essentially just wrappers around matplotlib and turtles.plotting functions.
• GLM class methods that are meant to be implemented by child classes are ignored.