fmvmm 2.0.0

Flexible Multivariate Mixture Model

FMVMM: Flexible Multivariate Mixture Model

FMVMM is a Python package providing a comprehensive collection of finite mixture models for various multivariate distributions. It is designed to offer flexibility in modeling both identical and non-identical mixture distributions, allowing users to apply advanced clustering techniques efficiently.

Features

• Implements finite mixtures of various multivariate distributions.
• Supports clustering using Dirichlet Mixture Models and mixtures of other non-identical distributions.
• Provides multiple model selection criteria such as AIC, BIC, and ICL.
• Includes efficient parameter estimation and standard error calculations.
• Example Jupyter notebooks available in the examples/ folder.

Mixture Models Included

• Dirichlet Mixture Model (DMM_Soft, DMM_Hard)
• Mixtures of Multivariate Generalized Hyperbolic Distributions (MixMGH)
• Mixtures of Skew Normal Distributions (SkewNormalMix)
• Mixtures of Skew T Distributions (SkewTMix)
• Mixtures of T Distributions (TMix)
• Mixtures of Skew Normal Contaminated Distributions (SkewContMix)
• Mixtures of Skew Slash Distributions (SkewSlashMix)
• Mixtures of Slash Distributions (SlashMix)
• Flexible Multivariate Mixture Model (FMVMM)
  • This model allows fitting all possible combinations of mixtures of different identical and non-identical distributions.

Distributions Included

• Multivariate Skew Normal
• Multivariate Normal
• Multivariate T
• Multivariate Generalized Skew T
• Multivariate Skew T
• Multivariate Hyperbolic
• Multivariate Normal Inverse Gaussian
• Multivariate Variance Gamma
• Multivariate Skew Slash
• Multivariate Slash
• Multivariate Skew Normal Contaminated

Installation

You can install FMVMM using:

pip install fmvmm

Usage

Each Python class in FMVMM provides the following methods:

from fmvmm.mixtures.DMM_Soft import DMM_Soft

model = DMM_Soft(n_clusters=3)
model.fit(data)  # Fit a mixture model
clusters = model.predict()  # Get cluster assignments
bic_value = model.bic()  # Compute Bayesian Information Criterion
aic_value = model.aic()  # Compute Akaike Information Criterion
icl_value = model.icl()  # Compute Integrated Complete Likelihood Criterion
pi, alpha = model.get_params()  # Get MLE of parameters
info_matrix, se = model.get_info_mat()  # Get information matrix and standard errors

For more detailed examples, see the Jupyter notebooks in the examples/ folder.

Citation

If you use FMVMM in your research, please cite the relevant papers:

1. Pal, Samyajoy, and Christian Heumann. "Clustering compositional data using Dirichlet mixture model." PLoS ONE 17, no. 5 (2022): e0268438. https://doi.org/10.1371/journal.pone.0268438.
2. Pal, Samyajoy, and Christian Heumann. "Gene coexpression analysis with Dirichlet mixture model: accelerating model evaluation through closed-form KL divergence approximation using variational techniques." International Workshop on Statistical Modelling (2024). https://doi.org/10.1007/978-3-031-65723-8_21.
3. Pal, Samyajoy, and Christian Heumann. "Revisiting Dirichlet Mixture Model: Unraveling Deeper Insights and Practical Applications." Statistical Papers 66, no. 1 (2025): 1-38. https://doi.org/10.1007/s00362-024-01627-0.
4. Pal, Samyajoy, and Christian Heumann. "Flexible Multivariate Mixture Models: A Comprehensive Approach for Modeling Mixtures of Non-Identical Distributions." International Statistical Review (2024). https://doi.org/10.1111/insr.12593.

License

FMVMM is open-source and distributed under the MIT License.

Contact

For any questions or contributions, feel free to reach out or open an issue on GitHub.