from math import log
from pgmpy.structure_score.log_likelihood import LogLikelihood
[docs]
class BIC(LogLikelihood):
r"""
BIC structure score for discrete Bayesian networks.
BIC, also known as the MDL score, balances discrete log-likelihood against model complexity. The local score
is computed as:
.. math::
\operatorname{BIC}(X_i, \Pi_i) = \ell(X_i, \Pi_i) - \frac{\log n}{2} q_i (r_i - 1),
where :math:`\ell(X_i, \Pi_i)` is the local discrete log-likelihood, :math:`n` is the number of rows in `self.data`,
:math:`q_i` is the number of parent configurations of :math:`\Pi_i`, and :math:`r_i` is the cardinality of
:math:`X_i`.
Parameters
----------
data : pandas.DataFrame
DataFrame where each column represents a discrete variable. Missing values should be set to `numpy.nan`.
state_names : dict, optional
Dictionary mapping each variable to its discrete states. If not specified, the unique values observed in the
data are used.
Examples
--------
>>> import pandas as pd
>>> from pgmpy.models import DiscreteBayesianNetwork
>>> from pgmpy.structure_score import BIC
>>> data = pd.DataFrame(
... {"A": [0, 1, 1, 0], "B": [1, 0, 1, 0], "C": [1, 1, 1, 0]}
... )
>>> model = DiscreteBayesianNetwork([("A", "B"), ("A", "C")])
>>> score = BIC(data)
>>> round(score.score(model), 3)
np.float64(-10.397)
>>> round(score.local_score("B", ("A",)), 3)
np.float64(-4.159)
Raises
------
ValueError
If the data contains non-discrete variables, or if the model variables are not present
in the data.
References
----------
.. [1] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009, Section 18.3.4-18.3.6.
.. [2] AM Carvalho, Scoring functions for learning Bayesian networks,
http://www.lx.it.pt/~asmc/pub/talks/09-TA/ta_pres.pdf
"""
_tags = {
"name": "bic-d",
"supported_datatype": "discrete",
"default_for": "discrete",
"is_parameteric": False,
}
def __init__(self, data, state_names=None):
super().__init__(data, state_names=state_names)
def _local_score(self, variable: str, parents: tuple[str, ...]) -> float:
sample_size = len(self.data)
ll, num_parents_states, var_cardinality = self._log_likelihood(variable=variable, parents=parents)
score = ll - 0.5 * log(sample_size) * num_parents_states * (var_cardinality - 1)
return score
