# Source code for pgmpy.estimators.StructureScore

```
#!/usr/bin/env python
from math import lgamma, log
import numpy as np
from scipy.special import gammaln
from pgmpy.estimators import BaseEstimator
class StructureScore(BaseEstimator):
def __init__(self, data, **kwargs):
"""
Abstract base class for structure scoring classes in pgmpy. Use any of the derived classes
K2Score, BDeuScore, BicScore or AICScore. Scoring classes are
used to measure how well a model is able to describe the given data set.
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.
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.
This sets the behavior of the `state_count`-method.
Reference
---------
Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 18.3
"""
super(StructureScore, self).__init__(data, **kwargs)
def score(self, model):
"""
Computes a score to measure how well the given `BayesianNetwork` fits
to the data set. (This method relies on the `local_score`-method that
is implemented in each subclass.)
Parameters
----------
model: BayesianNetwork instance
The Bayesian network that is to be scored. Nodes of the BayesianNetwork need to coincide
with column names of data set.
Returns
-------
score: float
A number indicating the degree of fit between data and model
Examples
--------
>>> import pandas as pd
>>> import numpy as np
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.estimators import K2Score
>>> # create random data sample with 3 variables, where B and C are identical:
>>> data = pd.DataFrame(np.random.randint(0, 5, size=(5000, 2)), columns=list('AB'))
>>> data['C'] = data['B']
>>> K2Score(data).score(BayesianNetwork([['A','B'], ['A','C']]))
-24242.367348745247
>>> K2Score(data).score(BayesianNetwork([['A','B'], ['B','C']]))
-16273.793897051042
"""
score = 0
for node in model.nodes():
score += self.local_score(node, model.predecessors(node))
score += self.structure_prior(model)
return score
def structure_prior(self, model):
"""A (log) prior distribution over models. Currently unused (= uniform)."""
return 0
def structure_prior_ratio(self, operation):
"""Return the log ratio of the prior probabilities for a given proposed change to the DAG.
Currently unused (=uniform)."""
return 0
[docs]class K2Score(StructureScore):
def __init__(self, data, **kwargs):
"""
Class for Bayesian structure scoring for BayesianNetworks with Dirichlet priors.
The K2 score is the result of setting all Dirichlet hyperparameters/pseudo_counts to 1.
The `score`-method measures how well a model is able to describe the given data set.
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.
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.
This sets the behavior of the `state_count`-method.
References
---------
[1] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 18.3.4-18.3.6 (esp. page 806)
[2] AM Carvalho, Scoring functions for learning Bayesian networks,
http://www.lx.it.pt/~asmc/pub/talks/09-TA/ta_pres.pdf
"""
super(K2Score, self).__init__(data, **kwargs)
[docs] def local_score(self, variable, parents):
'Computes a score that measures how much a \
given variable is "influenced" by a given list of potential parents.'
var_states = self.state_names[variable]
var_cardinality = len(var_states)
parents = list(parents)
state_counts = self.state_counts(variable, parents, reindex=False)
num_parents_states = np.prod([len(self.state_names[var]) for var in parents])
counts = np.asarray(state_counts)
log_gamma_counts = np.zeros_like(counts, dtype=float)
# Compute log(gamma(counts + 1))
gammaln(counts + 1, out=log_gamma_counts)
# Compute the log-gamma conditional sample size
log_gamma_conds = np.sum(counts, axis=0, dtype=float)
gammaln(log_gamma_conds + var_cardinality, out=log_gamma_conds)
# Adjustments when using reindex=False as it drops columns of 0 state counts
gamma_counts_adj = (
(num_parents_states - counts.shape[1]) * var_cardinality * gammaln(1)
)
gamma_conds_adj = (num_parents_states - counts.shape[1]) * gammaln(
var_cardinality
)
score = (
np.sum(log_gamma_counts)
- np.sum(log_gamma_conds)
+ num_parents_states * lgamma(var_cardinality)
)
return score
[docs]class BDeuScore(StructureScore):
def __init__(self, data, equivalent_sample_size=10, **kwargs):
"""
Class for Bayesian structure scoring for BayesianNetworks with Dirichlet priors.
The BDeu score is the result of setting all Dirichlet hyperparameters/pseudo_counts to
`equivalent_sample_size/variable_cardinality`.
The `score`-method measures how well a model is able to describe the given data set.
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`.)
equivalent_sample_size: int (default: 10)
The equivalent/imaginary sample size (of uniform pseudo samples) for the dirichlet hyperparameters.
The score is sensitive to this value, runs with different values might be useful.
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.
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.
This sets the behavior of the `state_count`-method.
References
---------
[1] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 18.3.4-18.3.6 (esp. page 806)
[2] AM Carvalho, Scoring functions for learning Bayesian networks,
http://www.lx.it.pt/~asmc/pub/talks/09-TA/ta_pres.pdf
"""
self.equivalent_sample_size = equivalent_sample_size
super(BDeuScore, self).__init__(data, **kwargs)
[docs] def local_score(self, variable, parents):
'Computes a score that measures how much a \
given variable is "influenced" by a given list of potential parents.'
var_states = self.state_names[variable]
var_cardinality = len(var_states)
parents = list(parents)
state_counts = self.state_counts(variable, parents, reindex=False)
num_parents_states = np.prod([len(self.state_names[var]) for var in parents])
counts = np.asarray(state_counts)
# counts size is different because reindex=False is dropping columns.
counts_size = num_parents_states * len(self.state_names[variable])
log_gamma_counts = np.zeros_like(counts, dtype=float)
alpha = self.equivalent_sample_size / num_parents_states
beta = self.equivalent_sample_size / counts_size
# Compute log(gamma(counts + beta))
gammaln(counts + beta, out=log_gamma_counts)
# Compute the log-gamma conditional sample size
log_gamma_conds = np.sum(counts, axis=0, dtype=float)
gammaln(log_gamma_conds + alpha, out=log_gamma_conds)
# Adjustment because of missing 0 columns when using reindex=False for computing state_counts to save memory.
gamma_counts_adj = (
(num_parents_states - counts.shape[1])
* len(self.state_names[variable])
* gammaln(beta)
)
gamma_conds_adj = (num_parents_states - counts.shape[1]) * gammaln(alpha)
score = (
(np.sum(log_gamma_counts) + gamma_counts_adj)
- (np.sum(log_gamma_conds) + gamma_conds_adj)
+ num_parents_states * lgamma(alpha)
- counts_size * lgamma(beta)
)
return score
[docs]class BDsScore(BDeuScore):
def __init__(self, data, equivalent_sample_size=10, **kwargs):
"""
Class for Bayesian structure scoring for BayesianNetworks with
Dirichlet priors. The BDs score is the result of setting all Dirichlet
hyperparameters/pseudo_counts to
`equivalent_sample_size/modified_variable_cardinality` where for the
modified_variable_cardinality only the number of parent configurations
where there were observed variable counts are considered. The
`score`-method measures how well a model is able to describe the given
data set.
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`.)
equivalent_sample_size: int (default: 10)
The equivalent/imaginary sample size (of uniform pseudo samples) for the dirichlet
hyperparameters.
The score is sensitive to this value, runs with different values might be useful.
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.
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.
This sets the behavior of the `state_count`-method.
References
---------
[1] Scutari, Marco. An Empirical-Bayes Score for Discrete Bayesian Networks.
Journal of Machine Learning Research, 2016, pp. 438–48
"""
super(BDsScore, self).__init__(data, equivalent_sample_size, **kwargs)
[docs] def structure_prior_ratio(self, operation):
"""Return the log ratio of the prior probabilities for a given proposed change to
the DAG.
"""
if operation == "+":
return -log(2.0)
if operation == "-":
return log(2.0)
return 0
[docs] def structure_prior(self, model):
"""
Implements the marginal uniform prior for the graph structure where each arc
is independent with the probability of an arc for any two nodes in either direction
is 1/4 and the probability of no arc between any two nodes is 1/2."""
nedges = float(len(model.edges()))
nnodes = float(len(model.nodes()))
possible_edges = nnodes * (nnodes - 1) / 2.0
score = -(nedges + possible_edges) * log(2.0)
return score
[docs] def local_score(self, variable, parents):
'Computes a score that measures how much a \
given variable is "influenced" by a given list of potential parents.'
var_states = self.state_names[variable]
var_cardinality = len(var_states)
parents = list(parents)
state_counts = self.state_counts(variable, parents, reindex=False)
num_parents_states = np.prod([len(self.state_names[var]) for var in parents])
counts = np.asarray(state_counts)
# counts size is different because reindex=False is dropping columns.
counts_size = num_parents_states * len(self.state_names[variable])
log_gamma_counts = np.zeros_like(counts, dtype=float)
alpha = self.equivalent_sample_size / state_counts.shape[1]
beta = self.equivalent_sample_size / counts_size
# Compute log(gamma(counts + beta))
gammaln(counts + beta, out=log_gamma_counts)
# Compute the log-gamma conditional sample size
log_gamma_conds = np.sum(counts, axis=0, dtype=float)
gammaln(log_gamma_conds + alpha, out=log_gamma_conds)
# Adjustment because of missing 0 columns when using reindex=False for computing state_counts to save memory.
gamma_counts_adj = (
(num_parents_states - counts.shape[1])
* len(self.state_names[variable])
* gammaln(beta)
)
gamma_conds_adj = (num_parents_states - counts.shape[1]) * gammaln(alpha)
score = (
(np.sum(log_gamma_counts) + gamma_counts_adj)
- (np.sum(log_gamma_conds) + gamma_conds_adj)
+ state_counts.shape[1] * lgamma(alpha)
- counts_size * lgamma(beta)
)
return score
[docs]class BicScore(StructureScore):
def __init__(self, data, **kwargs):
"""
Class for Bayesian structure scoring for BayesianNetworks with
Dirichlet priors. The BIC/MDL score ("Bayesian Information Criterion",
also "Minimal Descriptive Length") is a log-likelihood score with an
additional penalty for network complexity, to avoid overfitting. The
`score`-method measures how well a model is able to describe the given
data set.
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.
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.
This sets the behavior of the `state_count`-method.
References
---------
[1] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 18.3.4-18.3.6 (esp. page 802)
[2] AM Carvalho, Scoring functions for learning Bayesian networks,
http://www.lx.it.pt/~asmc/pub/talks/09-TA/ta_pres.pdf
"""
super(BicScore, self).__init__(data, **kwargs)
[docs] def local_score(self, variable, parents):
'Computes a score that measures how much a \
given variable is "influenced" by a given list of potential parents.'
var_states = self.state_names[variable]
var_cardinality = len(var_states)
parents = list(parents)
state_counts = self.state_counts(variable, parents, reindex=False)
sample_size = len(self.data)
num_parents_states = np.prod([len(self.state_names[var]) for var in parents])
counts = np.asarray(state_counts)
log_likelihoods = np.zeros_like(counts, dtype=float)
# Compute the log-counts
np.log(counts, out=log_likelihoods, where=counts > 0)
# Compute the log-conditional sample size
log_conditionals = np.sum(counts, axis=0, dtype=float)
np.log(log_conditionals, out=log_conditionals, where=log_conditionals > 0)
# Compute the log-likelihoods
log_likelihoods -= log_conditionals
log_likelihoods *= counts
score = np.sum(log_likelihoods)
score -= 0.5 * log(sample_size) * num_parents_states * (var_cardinality - 1)
return score
class AICScore(StructureScore):
def __init__(self, data, **kwargs):
"""
Class for Bayesian structure scoring for BayesianNetworks with
Dirichlet priors. The AIC score ("Akaike Information Criterion) is a log-likelihood score with an
additional penalty for network complexity, to avoid overfitting. The
`score`-method measures how well a model is able to describe the given
data set.
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.
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.
This sets the behavior of the `state_count`-method.
References
---------
[1] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 18.3.4-18.3.6 (esp. page 802)
[2] AM Carvalho, Scoring functions for learning Bayesian networks,
http://www.lx.it.pt/~asmc/pub/talks/09-TA/ta_pres.pdf
"""
super(AICScore, self).__init__(data, **kwargs)
def local_score(self, variable, parents):
'Computes a score that measures how much a \
given variable is "influenced" by a given list of potential parents.'
var_states = self.state_names[variable]
var_cardinality = len(var_states)
parents = list(parents)
state_counts = self.state_counts(variable, parents, reindex=False)
sample_size = len(self.data)
num_parents_states = np.prod([len(self.state_names[var]) for var in parents])
counts = np.asarray(state_counts)
log_likelihoods = np.zeros_like(counts, dtype=float)
# Compute the log-counts
np.log(counts, out=log_likelihoods, where=counts > 0)
# Compute the log-conditional sample size
log_conditionals = np.sum(counts, axis=0, dtype=float)
np.log(log_conditionals, out=log_conditionals, where=log_conditionals > 0)
# Compute the log-likelihoods
log_likelihoods -= log_conditionals
log_likelihoods *= counts
score = np.sum(log_likelihoods)
score -= num_parents_states * (var_cardinality - 1)
return score
```