Bayesian Estimator

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

Class used to compute parameters for a model using Bayesian Parameter Estimation. See MaximumLikelihoodEstimator for constructor parameters.

estimate_cpd(node, prior_type='BDeu', pseudo_counts=[], equivalent_sample_size=5, weighted=False)[source]

Method to estimate the CPD for a given variable.

Parameters:

  • node (int, string (any hashable python object)) – The name of the variable for which the CPD is to be estimated.

  • prior_type ('dirichlet', 'BDeu', 'K2',) –

    string indicting which type of prior to use for the model parameters. - If ‘prior_type’ is ‘dirichlet’, the following must be provided:

    ’pseudo_counts’ = dirichlet hyperparameters; a single number or 2-D array

    of shape (node_card, product of parents_card) with a “virtual” count for each variable state in the CPD. The virtual counts are added to the actual state counts found in the data. (if a list is provided, a lexicographic ordering of states is assumed)

    • If ‘prior_type’ is ‘BDeu’, then an ‘equivalent_sample_size’

      must be specified instead of ‘pseudo_counts’. This is equivalent to ‘prior_type=dirichlet’ and using uniform ‘pseudo_counts’ of equivalent_sample_size/(node_cardinality*np.prod(parents_cardinalities)).

    • A prior_type of ‘K2’ is a shorthand for ‘dirichlet’ + setting every pseudo_count to 1, regardless of the cardinality of the variable.

  • weighted (bool) – If weighted=True, the data must contain a _weight column specifying the weight of each datapoint (row). If False, assigns an equal weight to each datapoint.

Returns:

CPD – The estimated CPD for node.

Return type:

TabularCPD

Examples

>>> import pandas as pd
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.estimators import BayesianEstimator
>>> data = pd.DataFrame(data={'A': [0, 0, 1], 'B': [0, 1, 0], 'C': [1, 1, 0]})
>>> model = BayesianNetwork([('A', 'C'), ('B', 'C')])
>>> estimator = BayesianEstimator(model, data)
>>> cpd_C = estimator.estimate_cpd('C', prior_type="dirichlet",
...                                pseudo_counts=[[1, 1, 1, 1],
...                                               [2, 2, 2, 2]])
>>> print(cpd_C)
╒══════╤══════╤══════╤══════╤════════════════════╕
│ A    │ A(0) │ A(0) │ A(1) │ A(1)               │
├──────┼──────┼──────┼──────┼────────────────────┤
│ B    │ B(0) │ B(1) │ B(0) │ B(1)               │
├──────┼──────┼──────┼──────┼────────────────────┤
│ C(0) │ 0.25 │ 0.25 │ 0.5  │ 0.3333333333333333 │
├──────┼──────┼──────┼──────┼────────────────────┤
│ C(1) │ 0.75 │ 0.75 │ 0.5  │ 0.6666666666666666 │
╘══════╧══════╧══════╧══════╧════════════════════╛
get_parameters(prior_type='BDeu', equivalent_sample_size=5, pseudo_counts=None, n_jobs=1, weighted=False)[source]

Method to estimate the model parameters (CPDs).

Parameters:

  • prior_type ('dirichlet', 'BDeu', or 'K2') –

    string indicting which type of prior to use for the model parameters. - If ‘prior_type’ is ‘dirichlet’, the following must be provided:

    ’pseudo_counts’ = dirichlet hyperparameters; a single number or a dict containing, for each

    variable, a 2-D array of the shape (node_card, product of parents_card) with a “virtual” count for each variable state in the CPD, that is added to the state counts. (lexicographic ordering of states assumed)

    • If ‘prior_type’ is ‘BDeu’, then an ‘equivalent_sample_size’

      must be specified instead of ‘pseudo_counts’. This is equivalent to ‘prior_type=dirichlet’ and using uniform ‘pseudo_counts’ of equivalent_sample_size/(node_cardinality*np.prod(parents_cardinalities)) for each node. ‘equivalent_sample_size’ can either be a numerical value or a dict that specifies the size for each variable separately.

    • A prior_type of ‘K2’ is a shorthand for ‘dirichlet’ + setting every pseudo_count to 1,

      regardless of the cardinality of the variable.

  • equivalent_sample_size (int) – Refer prior_type for more details.

  • pseudo_counts (int (default: None)) – Refer prior_type for more details.

  • n_jobs (int (default: 1)) – Number of jobs to run in parallel. Default: 1. Using n_jobs > 1 for small models might be slower.

  • weighted (bool) – If weighted=True, the data must contain a _weight column specifying the weight of each datapoint (row). If False, assigns an equal weight to each datapoint.

Returns:

parameters – List of TabularCPDs, one for each variable of the model

Return type:

list

Examples

>>> import numpy as np
>>> import pandas as pd
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.estimators import BayesianEstimator
>>> values = pd.DataFrame(np.random.randint(low=0, high=2, size=(1000, 4)),
...                       columns=['A', 'B', 'C', 'D'])
>>> model = BayesianNetwork([('A', 'B'), ('C', 'B'), ('C', 'D')])
>>> estimator = BayesianEstimator(model, values)
>>> estimator.get_parameters(prior_type='BDeu', equivalent_sample_size=5)
[<TabularCPD representing P(C:2) at 0x7f7b534251d0>,
<TabularCPD representing P(B:2 | C:2, A:2) at 0x7f7b4dfd4da0>,
<TabularCPD representing P(A:2) at 0x7f7b4dfd4fd0>,
<TabularCPD representing P(D:2 | C:2) at 0x7f7b4df822b0>]