# coding:utf-8
from itertools import chain
import numpy as np
from joblib import Parallel, delayed
from pgmpy.estimators import ParameterEstimator
from pgmpy.factors import FactorDict
from pgmpy.factors.discrete import TabularCPD
from pgmpy.models import BayesianNetwork, JunctionTree
[docs]
class MaximumLikelihoodEstimator(ParameterEstimator):
"""
Class used to compute parameters for a model using Maximum Likelihood Estimation.
Parameters
----------
model: A pgmpy.models.BayesianNetwork or pgmpy.models.JunctionTree 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.
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)
"""
def __init__(self, model, data, **kwargs):
if not isinstance(model, BayesianNetwork) and not isinstance(
model, JunctionTree
):
raise NotImplementedError(
"Maximum Likelihood Estimate is only implemented for BayesianNetwork and JunctionTree"
)
elif set(model.nodes()) > set(data.columns):
if isinstance(model, BayesianNetwork):
raise ValueError(
f"Found latent variables: {model.latents}. Maximum Likelihood doesn't support latent variables, please use ExpectationMaximization"
)
else:
raise ValueError(
"Nodes detected in the model that are not present in the dataset. "
+ "Refine the model so that all parameters can be estimated from the data."
)
super(MaximumLikelihoodEstimator, self).__init__(model, data, **kwargs)
[docs]
def get_parameters(self, n_jobs=1, weighted=False):
"""
Method to estimate the model parameters using Maximum Likelihood Estimation.
Parameters
----------
n_jobs: int (default: 1)
Number of jobs to run in parallel. Default: 1 uses all the processors.
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
-------
Estimated parameters: list or pgmpy.factors.FactorDict
List of pgmpy.factors.discrete.TabularCPDs, one for each variable of the model
Or a FactorDict representing potential values of a Junction Tree
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>]
"""
if isinstance(self.model, JunctionTree):
return self.estimate_potentials()
parameters = Parallel(n_jobs=n_jobs)(
delayed(self.estimate_cpd)(node, weighted) for node in self.model.nodes()
)
# TODO: A hacky solution to return correct value for the chosen backend. Ref #1675
parameters = [p.copy() for p in parameters]
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
-------
Estimated CPD: pgmpy.factors.discrete.TabularCPD
Estimated CPD for `node`.
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.iloc[:, (state_counts.values == 0).all(axis=0)] = 1.0
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
[docs]
def estimate_potentials(self):
"""
Implements Iterative Proportional Fitting to estimate potentials specifically
for a Decomposable Undirected Graphical Model. Decomposability is enforced
by using a Junction Tree.
Returns
-------
Estimated potentials: pgmpy.factors.FactorDict
Estimated potentials for the entire graphical model.
References
---------
[1] Kevin P. Murphy, ML Machine Learning - A Probabilistic Perspective
Algorithm 19.2 Iterative Proportional Fitting algorithm for tabular MRFs & Section 19.5.7.4 IPF for decomposable graphical models.
[2] Eric P. Xing, Meng Song, Li Zhou, Probabilistic Graphical Models 10-708, Spring 2014.
https://www.cs.cmu.edu/~epxing/Class/10708-14/scribe_notes/scribe_note_lecture8.pdf.
Examples
--------
>>> import pandas as pd
>>> from pgmpy.models import JunctionTree
>>> from pgmpy.estimators import MaximumLikelihoodEstimator
>>> data = pd.DataFrame(data={'A': [0, 0, 1], 'B': [0, 1, 0], 'C': [1, 1, 0]})
>>> model = JunctionTree()
>>> model.add_edges_from([(("A", "C"), ("B", "C"))])
>>> potentials = MaximumLikelihoodEstimator(model, data).estimate_potentials()
>>> print(potentials[("A", "C")])
+------+------+------------+
| A | C | phi(A,C) |
+======+======+============+
| A(0) | C(0) | 0.0000 |
+------+------+------------+
| A(0) | C(1) | 0.6667 |
+------+------+------------+
| A(1) | C(0) | 0.3333 |
+------+------+------------+
| A(1) | C(1) | 0.0000 |
+------+------+------------+
>>> print(potentials[("B", "C")])
+------+------+------------+
| B | C | phi(B,C) |
+======+======+============+
| B(0) | C(0) | 1.0000 |
+------+------+------------+
| B(0) | C(1) | 0.5000 |
+------+------+------------+
| B(1) | C(0) | 0.0000 |
+------+------+------------+
| B(1) | C(1) | 0.5000 |
+------+------+------------+
"""
if not isinstance(self.model, JunctionTree):
raise NotImplementedError(
"Iterative Proportional Fitting is only implemented for Junction Trees."
)
if not hasattr(self.model, "clique_beliefs"):
raise NotImplementedError(
"A model containing clique beliefs is required to estimate parameters."
)
clique_beliefs = self.model.clique_beliefs
if not isinstance(clique_beliefs, FactorDict):
raise TypeError(
"`UndirectedMaximumLikelihoodEstimator.model.clique_beliefs` must be a `FactorDict`."
)
# These are the variables as represented by the `JunctionTree`.
cliques = list(clique_beliefs.keys())
empirical_marginals = FactorDict.from_dataframe(df=self.data, marginals=cliques)
potentials = FactorDict({})
seen = set()
# ML Machine Learning - A Probabilistic Perspective
# Chapter 19, Algorithm 19.2, Page 682:
# Update each clique by multiplying the potential value by
# the ratio of the empirical counts over expected counts.
# Since the potential values are equal to the expected counts
# for a JunctionTree, we can simplify this to just the empirical counts.
# This is also described in section 19.5.7.4.
for clique in cliques:
# Calculate the running sepset between the new clique and all of the
# variables we have previously seen.
variables = tuple(set(clique) - seen)
seen.update(clique)
potentials[clique] = empirical_marginals[clique]
# Divide out the sepset.
if variables:
marginalized = empirical_marginals[clique].marginalize(
variables=variables, inplace=False
)
potentials[clique] = potentials[clique] / marginalized
return potentials
