Mmhc Estimator

class pgmpy.estimators.MmhcEstimator(data, **kwargs)[source]

Implements the MMHC hybrid structure estimation procedure for learning BayesianNetworks from discrete data.

Parameters:

  • data (pandas DataFrame object) – dataframe object where each column represents one variable. (If some values in the data are missing the data cells should be set to numpy.nan. Note that pandas converts each column containing numpy.nan`s to dtype `float.)

  • state_names (dict (optional)) – A dict indicating, for each variable, the discrete set of states (or values) that the variable can take. If unspecified, the observed values in the data set are taken to be the only possible states.

References

Tsamardinos et al., The max-min hill-climbing Bayesian network structure learning algorithm (2005) http://www.dsl-lab.org/supplements/mmhc_paper/paper_online.pdf

estimate(scoring_method=None, tabu_length=10, significance_level=0.01)[source]

Estimates a DiscreteBayesianNetwork for the data set, using MMHC. First estimates a graph skeleton using MMPC and then orients the edges using score-based local search (hill climbing).

Parameters:

  • significance_level (float, default: 0.01) – The significance level to use for conditional independence tests in the data set. See mmpc-method.

  • scoring_method (instance of a Scoring method (default: BDeu)) – The method to use for scoring during Hill Climb Search. Can be an instance of any of the scoring methods implemented in pgmpy.

  • tabu_length (int) – If provided, the last tabu_length graph modifications cannot be reversed during the search procedure. This serves to enforce a wider exploration of the search space. Default value: 100.

Returns:

Estimated model – The estimated model without the parameterization.

Return type:

pgmpy.base.DAG

References

Tsamardinos et al., The max-min hill-climbing Bayesian network structure learning algorithm (2005), Algorithm 3 http://www.dsl-lab.org/supplements/mmhc_paper/paper_online.pdf

Examples

>>> import pandas as pd
>>> import numpy as np
>>> from pgmpy.estimators import MmhcEstimator
>>> data = pd.DataFrame(
...     np.random.randint(0, 2, size=(2500, 4)), columns=list("XYZW")
... )
>>> data["sum"] = data.sum(axis=1)
>>> est = MmhcEstimator(data)
>>> model = est.estimate()
>>> print(model.edges())
[('Z', 'sum'), ('X', 'sum'), ('W', 'sum'), ('Y', 'sum')]
mmpc(significance_level=0.01)[source]

Estimates a graph skeleton (UndirectedGraph) for the data set, using then MMPC (max-min parents-and-children) algorithm.

Parameters:

significance_level (float, default=0.01) –

The significance level to use for conditional independence tests in the data set.

significance_level is the desired Type 1 error probability of falsely rejecting the null hypothesis that variables are independent, given that they are. The lower significance_level, the less likely we are to accept dependencies, resulting in a sparser graph.

Returns:

  • skeleton (pgmpy.base.UndirectedGraph) – An estimate for the undirected graph skeleton of the BN underlying the data.

  • seperating_sets (dict) – A dict containing for each pair of not directly connected nodes a seperating set (“witnessing set”) of variables that makes then conditionally independent. (needed for edge orientation)

References

Tsamardinos et al., The max-min hill-climbing Bayesian network structure learning algorithm (2005), Algorithm 1 & 2 http://www.dsl-lab.org/supplements/mmhc_paper/paper_online.pdf

Examples

>>> import pandas as pd
>>> import numpy as np
>>> from pgmpy.estimators import MmhcEstimator
>>> data = pd.DataFrame(
...     np.random.randint(0, 2, size=(5000, 5)), columns=list("ABCDE")
... )
>>> data["F"] = data["A"] + data["B"] + data["C"]
>>> est = PC(data)
>>> skel, sep_sets = est.estimate_skeleton()
>>> skel.edges()
[('A', 'F'), ('B', 'F'), ('C', 'F')]
>>> # all independencies are unconditional:
>>> sep_sets
{('D', 'A'): (), ('C', 'A'): (), ('C', 'E'): (), ('E', 'F'): (), ('B', 'D'): (),
 ('B', 'E'): (), ('D', 'F'): (), ('D', 'E'): (), ('A', 'E'): (), ('B', 'A'): (),
 ('B', 'C'): (), ('C', 'D'): ()}
>>> data = pd.DataFrame(
...     np.random.randint(0, 2, size=(5000, 3)), columns=list("XYZ")
... )
>>> data["X"] += data["Z"]
>>> data["Y"] += data["Z"]
>>> est = PC(data)
>>> skel, sep_sets = est.estimate_skeleton()
>>> skel.edges()
[('X', 'Z'), ('Y', 'Z')]
>>> # X, Y dependent, but conditionally independent given Z:
>>> sep_sets
{('X', 'Y'): ('Z',)}