turtles-glms 1.1.1

GLMs in Python.

PyGLMs

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

I created this package as a personal 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-glms (I like turtles).

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 code base. 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 child class and calling its fit() method.

model = PoissonReg(
    method="newton",
    learning_rate=0.01
)
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

Clone the repo and create your virtual environment from project root. This project requires Python 3.10+.

uv venv
source .venv/Scripts/activate || source .venv/bin/activate
uv sync --all-extras
pre-commit install

Adding GLMs

To add a new GLM class, inherit from the GLM parent class (see PoissonReg and LogReg for examples). The GLM parent class provides a framework for implementing new models and should be used whenever possible. Planned but currently unimplemented GLMs include Negative Binomial, Gamma, and Tweedie.

The GLM parent class defines several empty instance methods that are intended to be overridden by child classes:

1. self._objective_func: The objective function to be minimized.
2. self._link_func: The GLM's link function (e.g., the logit link for Logistic Regression).
3. self._grad_func: The first derivative of the loss function, used by some optimization algorithms.
4. self._hess_func: The second derivative of the loss function, used by some optimization algorithms.

The implementations in the existing child classes are intentionally written for clarity to help readers and developers understand the underlying mathematics. This design also makes implementing new GLMs pretty straightforward.

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.