Dynamic Expectation-Maximization algorithms for Mixed-type Data

This repository provides tools and algorithms for the estimation of mixture models for mixed-type data. The algorithms jointly estimate the model parameters and the number of classes in the model.

This repository corresponds to the implementation of the paper 📄 Solange Pruilh, Stéphanie Allassonnière. Dynamic Expectation-Maximization algorithms for Mixed-type Data. 2024..

Requirements

The code was tested on Python 3.12.4.

With uv (recommended — installs Python and all dependencies in one step):

pip install uv          # install uv once, globally
uv sync                 # creates .venv/ and installs all dependencies
uv run python           # run any command inside the environment

With conda (alternative):

conda create -n DEM_MD --file requirements.txt
conda activate DEM_MD
pip install -e .

Quick start

import numpy as np
from dem_md import GaussianDEMMD

# Continuous-only data
X = np.random.randn(200, 4)
model = GaussianDEMMD()
labels = model.fit_predict(X)

# Mixed data (continuous + one Bernoulli discrete feature)
X_mixed = np.hstack([np.random.randn(200, 3), np.random.randint(0, 2, (200, 1))])
model_mixed = GaussianDEMMD(
    type_discrete_features=["Bernoulli"],
    index_discrete_features=[np.array([3])],
)
labels_mixed = model_mixed.fit_predict(X_mixed)

See the tutorial notebook for detailed experiments on different use cases.

Code

Several classes are provided, corresponding to DEM-MD algorithms to estimate different mixture models.

• DEM_MD_gaussian.py, DEM_MD_student.py and DEM_MD_sal.py contain classes to estimate mixture models with respectively Gaussian (GaussianDEMMD), Student (StudentDEMMD) and Shifted Asymmetric Laplace (SALDEMMD) distributions.
• These three DEM-MD classes are based on base_DEM_MD.py, base_MD.py and base.py which are parent classes.
• utils folder contains several files with tool functions: sampling.py for sampling datasets, calculation.py for miscellaneous computations, and validation.py for input validation.
• history.py contains the Historic class, which is directly instantiated into DEM-MD classes.
• Notations.md documents the variable naming conventions used throughout the codebase.

Citation

@unpublished{pruilh2024demmd,
  title     = {Dynamic Expectation-Maximization algorithms for Mixed-type Data},
  author    = {Pruilh, Solange and Allassonni{\`e}re, St{\'e}phanie},
  year      = {2024},
  note      = {Preprint},
  url       = {https://hal.science/hal-04510689},
}