from math import lgamma
import numpy as np
from scipy.special import gammaln
from pgmpy.structure_score._base import BaseStructureScore
[docs]
class K2(BaseStructureScore):
r"""
K2 structure score for discrete Bayesian networks using uniform Dirichlet priors.
The K2 score evaluates a Bayesian network structure on fully discrete data under a Dirichlet prior in which all
pseudo-counts are equal to 1. The local score is computed as:
.. math::
\operatorname{K2}(X_i, \Pi_i) = \sum_{j=1}^{q_i} \left[ \log \Gamma(r_i)
- \log \Gamma(N_{ij} + r_i) + \sum_{k=1}^{r_i} \log \Gamma(N_{ijk} + 1) \right],
where :math:`r_i` is the cardinality of :math:`X_i`, :math:`q_i` is the number of parent configurations of
:math:`\Pi_i`, :math:`N_{ijk}` is the count of :math:`X_i = k` in parent configuration :math:`j`, and
:math:`N_{ij} = \sum_{k=1}^{r_i} N_{ijk}`.
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 K2
>>> 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 = K2(data)
>>> round(score.score(model), 3)
np.float64(-9.875)
>>> round(score.local_score("B", ("A",)), 3)
np.float64(-3.584)
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": "k2",
"supported_datatype": "discrete",
"default_for": None,
"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:
var_cardinality = len(self.state_names[variable])
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)
gammaln(counts + 1, out=log_gamma_counts)
log_gamma_conds = np.sum(counts, axis=0, dtype=float)
gammaln(log_gamma_conds + var_cardinality, out=log_gamma_conds)
score = np.sum(log_gamma_counts) - np.sum(log_gamma_conds) + num_parents_states * lgamma(var_cardinality)
return score
