imm is a Python package for Bayesian MCMC inference in infinite mixture models. It is partially implemented in Cython for speed.

imm's main purpose is the clustering of multidimensional data in cases in which the number of clusters is not exactly known.

Currently, imm supports the following nonparametric models:

• the Dirichlet process (DP) mixture model and
• the mixture of finite mixtures (MFM) model.

The base measure can be either

• a multivariate normal distribution with a conjugate normal-Wishart prior or
• a multivariate normal with a conditionally conjugate normal-Wishart prior.

I will release proper documentation eventually. For now, have a look at the tutorial section below.

To install imm manually from the GitHub repository, clone it and do python setup.py install --user. Required are recent Cython and SciPy installations.

Below I demonstrate how to address a simple inference problem in imm.

import imm

mm = imm.models.ConjugateGaussianMixture(
    xi=[0.,0.],
    rho=.1,
    beta=2.5,
    W=[[1.5,.5],[.5,1.5]])

pm = imm.models.DP(mm, alpha=1.25, seed=1)

x_n, c_n = pm.draw(size=2000)

This will generate data of the following form:

Now we will try to infer the labels from the data:

s = imm.samplers.CollapsedSAMSSampler(pm, max_iter=500, warmup=0)

c_n_sams, _ = pm.infer(x_n, sampler=s)

The result, c_n_sams, is very similar to the original set of labels, c_n:

Each of the 500 iterations produces a set of labels. This process can be visualized as an animation:

The algorithm manages to find most of the clusters already in the first couple of iterations. The noisy switching of some of the labels demonstrates the remaining uncertainty of the model predictions, which is inherent to the Bayesian approach.

Credit goes to Hanna Wallach (UMass Amherst), whose DPMM project laid the foundation for the present code. The unified approach, the application to (conditionally) conjugate Gaussian mixture models, the mixture of finite mixtures model, and the SAMS sampler is my doing.

Although the code underwent and continues to undergo significant testing, please understand that I cannot give a guarantee that it is correct or will produce correct results. If you find an error, open an issue or drop me an email at [email protected].