# coding:utf-8
from itertools import chain
import numpy as np
from joblib import Parallel, delayed
from pgmpy.estimators import ParameterEstimator
from pgmpy.factors.discrete import TabularCPD
from pgmpy.models import BayesianNetwork
[docs]class MaximumLikelihoodEstimator(ParameterEstimator):
def __init__(self, model, data, **kwargs):
"""
Class used to compute parameters for a model using Maximum Likelihood Estimation.
Parameters
----------
model: A pgmpy.models.BayesianNetwork instance
data: pandas DataFrame object
DataFrame object with column names identical to the variable names of the network.
(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
that the variable can take. If unspecified, the observed values
in the data set are taken to be the only possible states.
complete_samples_only: bool (optional, default `True`)
Specifies how to deal with missing data, if present. If set to `True` all rows
that contain `np.NaN` somewhere are ignored. If `False` then, for each variable,
every row where neither the variable nor its parents are `np.NaN` is used.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.estimators import MaximumLikelihoodEstimator
>>> data = pd.DataFrame(np.random.randint(low=0, high=2, size=(1000, 5)),
... columns=['A', 'B', 'C', 'D', 'E'])
>>> model = BayesianNetwork([('A', 'B'), ('C', 'B'), ('C', 'D'), ('B', 'E')])
>>> estimator = MaximumLikelihoodEstimator(model, data)
"""
if not isinstance(model, BayesianNetwork):
raise NotImplementedError(
"Maximum Likelihood Estimate is only implemented for BayesianNetwork"
)
elif set(model.nodes()) > set(data.columns):
raise ValueError(
f"Maximum Likelihood Estimator works only for models with all observed variables. Found latent variables: {model.latents}."
)
super(MaximumLikelihoodEstimator, self).__init__(model, data, **kwargs)
[docs] def get_parameters(self, n_jobs=-1, weighted=False):
"""
Method to estimate the model parameters (CPDs) using Maximum Likelihood
Estimation.
Parameters
----------
n_jobs: int (default: -1)
Number of jobs to run in parallel. Default: -1 uses all the processors.
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
List of TabularCPDs, one for each variable of the model
n_jobs: int
Number of processes to spawn
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.estimators import MaximumLikelihoodEstimator
>>> 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 = MaximumLikelihoodEstimator(model, values)
>>> estimator.get_parameters()
[<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>]
"""
parameters = Parallel(n_jobs=n_jobs, prefer="threads")(
delayed(self.estimate_cpd)(node, weighted) for node in self.model.nodes()
)
return parameters
[docs] def estimate_cpd(self, node, weighted=False):
"""
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.
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: TabularCPD
Examples
--------
>>> import pandas as pd
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.estimators import MaximumLikelihoodEstimator
>>> data = pd.DataFrame(data={'A': [0, 0, 1], 'B': [0, 1, 0], 'C': [1, 1, 0]})
>>> model = BayesianNetwork([('A', 'C'), ('B', 'C')])
>>> cpd_A = MaximumLikelihoodEstimator(model, data).estimate_cpd('A')
>>> print(cpd_A)
╒══════╤══════════╕
│ A(0) │ 0.666667 │
├──────┼──────────┤
│ A(1) │ 0.333333 │
╘══════╧══════════╛
>>> cpd_C = MaximumLikelihoodEstimator(model, data).estimate_cpd('C')
>>> print(cpd_C)
╒══════╤══════╤══════╤══════╤══════╕
│ A │ A(0) │ A(0) │ A(1) │ A(1) │
├──────┼──────┼──────┼──────┼──────┤
│ B │ B(0) │ B(1) │ B(0) │ B(1) │
├──────┼──────┼──────┼──────┼──────┤
│ C(0) │ 0.0 │ 0.0 │ 1.0 │ 0.5 │
├──────┼──────┼──────┼──────┼──────┤
│ C(1) │ 1.0 │ 1.0 │ 0.0 │ 0.5 │
╘══════╧══════╧══════╧══════╧══════╛
"""
state_counts = self.state_counts(node, weighted=weighted)
# if a column contains only `0`s (no states observed for some configuration
# of parents' states) fill that column uniformly instead
state_counts.loc[:, (state_counts == 0).all()] = 1
parents = sorted(self.model.get_parents(node))
parents_cardinalities = [len(self.state_names[parent]) for parent in parents]
node_cardinality = len(self.state_names[node])
# Get the state names for the CPD
state_names = {node: list(state_counts.index)}
if parents:
state_names.update(
{
state_counts.columns.names[i]: list(state_counts.columns.levels[i])
for i in range(len(parents))
}
)
cpd = TabularCPD(
node,
node_cardinality,
np.array(state_counts),
evidence=parents,
evidence_card=parents_cardinalities,
state_names={var: self.state_names[var] for var in chain([node], parents)},
)
cpd.normalize()
return cpd