Bayesian nonparametric machine learning for Python
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bnpy : Bayesian nonparametric machine learning for python.


This python module provides code for training popular clustering models on large datasets. We focus on Bayesian nonparametric models based on the Dirichlet process, but also provide parametric counterparts.

bnpy supports the latest online learning algorithms as well as standard offline methods. Our aim is to provide an inference platform that makes it easy for researchers and practitioners to compare models and algorithms.

Supported probabilistic models (aka allocation models)

  • Mixture models

    • FiniteMixtureModel : fixed number of clusters
    • DPMixtureModel : infinite number of clusters, via the Dirichlet process
  • Topic models (aka admixtures models)

    • FiniteTopicModel : fixed number of topics. This is Latent Dirichlet allocation.
    • HDPTopicModel : infinite number of topics, via the hierarchical Dirichlet process
  • Hidden Markov models (HMMs)

    • FiniteHMM : Markov sequence model with a fixture number of states
    • HDPHMM : Markov sequence models with an infinite number of states

    • grammar models
    • relational models

Supported data observation models (aka likelihoods)

  • Multinomial for bag-of-words data
    • Mult
  • Gaussian for real-valued vector data
    • Gauss : Full-covariance
    • DiagGauss : Diagonal-covariance
    • ZeroMeanGauss : Zero-mean, full-covariance
  • Auto-regressive Gaussian
    • AutoRegGauss

Supported learning algorithms:

  • Expectation-maximization (offline)
    • EM
  • Full-dataset variational Bayes (offline)
    • VB
  • Memoized variational (online)
    • moVB
  • Stochastic variational (online)
    • soVB

These are all variants of variational inference, a family of optimization algorithms. We plan to eventually support sampling methods (Markov chain Monte Carlo) too.

Example Gallery

You can find many examples of bnpy in action in our curated Example Gallery.

These same demos are also directly available as Python scrips inside the examples/ folder of the project Github repository.

Quick Start

You can use bnpy from a command line/terminal, or from within Python. Both options require specifying a dataset, an allocation model, an observation model (likelihood), and an algorithm. Optional keyword arguments with reasonable defaults allow control of specific model hyperparameters, algorithm parameters, etc.

Below, we show how to call bnpy to train a 8 component Gaussian mixture model on a default toy dataset stored in a .csv file on disk. In both cases, log information is printed to stdout, and all learned model parameters are saved to disk.

Calling from the terminal/command-line

$ python -m bnpy.Run /path/to/my_dataset.csv FiniteMixtureModel Gauss EM --K 8 --output_path /tmp/my_dataset/results/

Calling directly from Python

import bnpy'/path/to/dataset.csv',
         'FiniteMixtureModel', 'Gauss', 'EM',
         K=8, output_path='/tmp/my_dataset/results/')

Advanced examples

Train Dirichlet-process Gaussian mixture model (DP-GMM) via full-dataset variational algorithm (aka "VB" for variational Bayes).

python -m bnpy.Run /path/to/dataset.csv DPMixtureModel Gauss VB --K 8

Train DP-GMM via memoized variational, with birth and merge moves, with data divided into 10 batches.

python -m bnpy.Run /path/to/dataset.csv DPMixtureModel Gauss memoVB --K 8 --nBatch 10 --moves birth,merge

Quick help

# print help message for required arguments
python -m bnpy.Run --help 

# print help message for specific keyword options for Gaussian mixture models
python -m bnpy.Run /path/to/dataset.csv FiniteMixtureModel Gauss EM --kwhelp


To use bnpy for the first time, follow the documentation's Installation Instructions.


Lead developer

Mike Hughes

Post-doctoral researcher (Aug. 2016 - present)
School of Engineering and Applied Sciences
Harvard University

Faculty adviser

Erik Sudderth
Assistant Professor
Brown University, Dept. of Computer Science


  • Soumya Ghosh
  • Dae Il Kim
  • Geng Ji
  • William Stephenson
  • Sonia Phene
  • Gabe Hope
  • Leah Weiner
  • Alexis Cook
  • Mert Terzihan
  • Mengrui Ni
  • Jincheng Li

Academic References

Conference publications based on BNPy

NIPS 2015 HDP-HMM paper

Our NIPS 2015 paper describes inference algorithms that can add or remove clusters for the sticky HDP-HMM.

AISTATS 2015 HDP topic model paper

Our AISTATS 2015 paper describes our algorithms for HDP topic models.

  • "Reliable and scalable variational inference for the hierarchical Dirichlet process." Michael C. Hughes, Dae Il Kim, and Erik B. Sudderth. AISTATS 2015. [paper] [supplement] [bibtex]

NIPS 2013 DP mixtures paper

Our NIPS 2013 paper introduced memoized variational inference algorithm, and applied it to Dirichlet process mixture models.

  • "Memoized online variational inference for Dirichlet process mixture models." Michael C. Hughes and Erik B. Sudderth. NIPS 2013. [paper] [supplement] [bibtex]

Workshop papers

Our short paper from a workshop at NIPS 2014 describes the vision for bnpy as a general purpose inference engine.

  • "bnpy: Reliable and scalable variational inference for Bayesian nonparametric models." Michael C. Hughes and Erik B. Sudderth. Probabilistic Programming Workshop at NIPS 2014. [paper]

Target Audience

Primarly, we intend bnpy to be a platform for researchers. By gathering many learning algorithms and popular models in one convenient, modular repository, we hope to make it easier to compare and contrast approaches. We also hope that the modular organization of bnpy enables researchers to try out new modeling ideas without reinventing the wheel.