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GamelanPy is a python implementation of GAMELAN (Genereative Model for Energy LANscape) algorithm. This algorithm is for learning a sparse Gaussian Mixture Model for structural fluctuations of a protein, but can also be used for other data where the original data can be assumed to follow a mixture of Gaussian distributions. GamelanPy supports options for sub-sampling methods for scalability and nonparanormal distributions for richer family of distributions than Gaussians. This package contains a pure python library and scripts for the command-line usages. For more detail on the algorithms, please refer to Efficient Learning of Sparse Gaussian Mixture Model of Protein Conformational Substates.


GamelanPy is tested to work under Python 2.7 (not tested in Python 3.x) The required dependencies are:

  • numpy >= 1.6.0
  • scipy >= 0.13.0
  • scikit-learn >= 0.16.0

and the core class and functions in the library are built on top of the scikit-learn's GMM class.

GamelanPy is a pure python module, and does not need to be compiled with other compilers.


It is recommended to install GamelanPy with pip:

pip install gamelanpy

As this package uses distutils, you also install GamelanPy by downloading the source and running:

cd /path/to/source
python install

Code and Repository

The source code is maintained in the github repository:

and you can clone the most recent status of the package by running:

git clone


Python Library


SparseGMM class is a main class for a sparse Gaussian Mixture Model. The snippet below is a simple code to create SparseGMM object and learn a model:

from gamelanpy import SparseGMM
s_gmm = SparseGMM(n_components=3), 'coreset', 1000)

User must specify the number of components and the type of distributions when creating the SparseGMM object:

  • n_components: Required. int.
  • nonparanormal: Optional, default is False. When nonparanoraml is True, this object represents a mixture of sparse nonparanormal distributions, and the learning process takes extra step for estimation of CDF (explained below). performs the structure and parameter learning of the model, and there are number of options:

  • subsample_method: Required. 'coreset', 'coreset2', 'uniform', or 'None'
    • 'coreset': Use coreset sampling for cluster identification, and use the original dataset to learn a sparse Gaussian for each cluster.
    • 'coreset2': Use coreset sampling for cluster identification, and use only coreset samples to learn a sparse Gaussian for each cluster. Recommended only if the runtime is the main issue.
    • 'uniform': Use randomly chosen samples for cluster identification, and use the original dataset to learn a sparse Gaussian for each cluster.
    • 'None': Does not use any subsampling method.
  • subsample_size: Required. Size of the subsamples.
  • l1_penalty_range: Optional, [min_value, max_value] for l1_penalty parameter search for each cluster. The default is [0.0001, 10.0].
  • l1_search_depth: Optional. l1_penalty search is done by binary-search-like heuristic method using graphical lasso, and it repeats the narrowing the range for l1_penalty by the given number of steps. The default is 20.
  • l1_search_repeat: Optional. The heuristic method is not deterministic, so it is recommended to repeat the search several times and takes the average for the final l1_penalty parameter. The default is 10.
  • npn_sample_ratio: Only required when the SparseGMM object is for nonparanormal distributions. Estimation of CDF takes extra space complexity, so users can specify the ratio of the givens samples to use in estimating the CDF. The value must be in (0.0, 1.0].

Below are some of the examples using a combination of options:

  • coreset sampling method with coreset size=500

      s_gmm = gamelan.SparseGMM(n_components=3), 'coreset', 1000)
  • uniform (random) sampling with subsample size=1000

      s_gmm = gamelan.SparseGMM(n_components=3), 'uniform', 500)
  • coreset2 sampling method with coreset size=1000

      s_gmm = gamelan.SparseGMM(n_components=3), 'coreset2', 1000)
  • coreset sampling method to estimate a mixture of sparse nonparanormals

      s_gmm = gamelan.SparseGMM(n_components=3, nonparanormal=True), 'coreset', 1000)
  • search for the best number for the number of components using BIC score

      n_components_candidates = range(3, 6)
      bic_scores = []
      best_score = -np.inf
      best_model = None
      for n_comp in n_components_candidates:
          s_gmm = gamelan.SparseGMM(n_components=n_comp)
          # learn using coreset subsampling
, 'coreset', 1000)
          bic_score = s_gmm.bic(test)
          if bic_score > best_score:
              best_score = bic_score
              best_model = s_gmm

Prediction and Imputation

Once a model is learned, it can be used for prediction studies. The functions predict_missing_values() and sample_missing_values() can be used to predict the missing values in a given data and to sample the missing coordinates.

The incomplete data must be ndarray type where the missing values are NaN's.

Below is a simple code snippet using both functions:

from gamelanpy.imputation_util import predict_missing_values

# get the most probable values (mean in the conditional distribution)
complete_data = predict_missing_values(model, incomplete_data)

# sample the missing values using the conditional distribution
samples_data = sample_missing_values(model, incomplete_data, n_samples=10)

More example usages are in the example directory in the source.

Python Scripts

This package also contains python scripts that can be used from command-line. The scripts are installed when the package is installed.

This script is for learning a model using a data stored in csv format.

Usage: <num_components> <path_to_data> [options]
  • num_components: number of components for the model
  • path_to_data: path to the csv formatted data

Options for learning: These options are corresponding options in function, and refer to the above section for more explanations.

  • --l1-depth: l1_search_depth for l1_penalty parameter search.
  • --l1-min and --l1-max: min and max values for l1_parameter search.
  • --subsample-method: 'coreset', 'coreset2' or 'uniform'. When not specified, it does not use any subsampling method, and uses the whole samples for the learning
  • --subsample-size: the size of the subsamples. Required when the --subsample-method is specified.
  • --l1-search-repeat: Number of repeats for l1_penalty parameter search.
  • --l1-search-depth: Depth for the binary-search-like heuristic method for l1_penalty parameter search.
  • --npn-sample-ratio: When specified, the model assumes the nonparanormal distributions. If not specified, the model is for sparse Gaussians. Sample ratio between 0.0 to 1.0 for estimation step for learning nonparanormal distributions.

Options for storing the model: It is recommended to dump the whole model after the learning, but users can also specify parameters to store in separate files.

  • --save-model: Path to the file for the whole model. The model is stored in JSON format where ndarray is stored in base64 encoded values. When the model is stored with this option, it can be loaded later for script.
  • --save-covars: Path to the file for covariance matrices. The covariance matrices 3-dimensional ndarray, so it is reshaped to (n_components * n_vars, n_vars).
  • --save-covars: Path to the file for precision matrices. The precision matrices 3-dimensional ndarray, so it is reshaped to (n_components * n_vars, n_vars).
  • --save-means: Path to the file for mean vectors.
  • --save-weights: Path to the file for weights of components


# learn sparse GMM with coreset sampling with coreset size 500
# save model to model.json and save precision matrices to precs.csv 3 data.csv --subsample-method='coreset' --subsample-size=500 --save-model=model.json --save-precs=precs.csv

# learn sparse Nonparanormal mixture model with coreset sampling with coreset size 500 and sample ratio 0.5
# save model to model.json and save precision matrices to precs.csv 5 data.csv --subsample-method='coreset' --subsample-size=500 --npn-sample-ratio=0.5 --save-model=model.json

This script is for prediction or sampling of missing values in an incomplete data. The missing values in the incomplete data can be represented by NaN or ?.

Usage: <path_to_model_json> <path_to_incomplete_data> <path_to_output> [options]
  • path_to_model_json: path to the json file representing SparseGMM object. It is highly recommended to use json file generated by script.
  • path_to_incomplete_data: path to the incomplete data.
  • path_to_output: path to store the predicted values or sampled values.


  • --n-samples: The number of samples to generate for a single incomplete datapoint. Thus, when --n-samples=10 and there are 5 incomplete rows in the data, then the output has 50 rows, 5 for each incomplete data. If not specified, the script generates the most probable values, the mean values of the conditional distributions.


# predict the most probable values and fill in those values in output.csv model.json incomplete.csv output.csv

# sample the missing values and fill in those values in output.csv,
# 10 samples for each incomplete datapoint model.json incomplete.csv output.csv --n-samples=10


Any contribution is welcome!


Python implementation of GAMELAN (GrAphical Models of Energy LANscapes) algorithm




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