def BDeu(bn, data, ess=1, ed=None):
"""
Unique Bayesian score with the property that I-equivalent
networks have the same score.
As Data Rows -> infinity, BDe score converges to the BIC score.
Nijk_prime = ess/len(bn.cpt(rv))
Arguments
---------
*bn* : a BayesNet object
Needed to get the parent relationships, etc.
*data* : a numpy ndarray
Needed to learn the empirical distribuion
*ess* : an integer
Equivalent sample size
*ed* : an EmpiricalDistribution object
Used to cache multiple lookups in structure learning.
Notes
-----
*a_ijk* : a vector
The number of times where x_i=k | parents(x_i)=j -> i.e. the mle counts
*a_ij* : a vector summed over k's in a_ijk
*n_ijk* : a vector prior (sample size or calculation)
ess/(card(x_i)*len(cpt(x_i)/card(x_i))) for x_i for BDe metric
*n_ij* : a vector prior summed over k's in n_ijk
"""
counts_dict = mle_fast(bn, data, counts=True, np=True)
a_ijk = []
bdeu = 1
for rv, value in counts_dict.items():
nijk = value['cpt']
nijk_prime = ess / len(nijk)
k2 *= gamma(nijk + nijk_prime) / gamma(nijk_prime)
nij_prime = nijk_prime * (len(cpt) / bn.card(rv))
nij = np.mean(nijk.reshape(-1, bn.card(rv)),
axis=1) # sum along parents
k2 *= gamma(nij_prime) / gamma(nij + nij_prime)
return bdeu
def BDeu(bn, data, ess=1, ed=None): """ Unique Bayesian score with the property that I-equivalent networks have the same score. As Data Rows -> infinity, BDe score converges to the BIC score. Nijk_prime = ess/len(bn.cpt(rv)) Arguments --------- *bn* : a BayesNet object Needed to get the parent relationships, etc. *data* : a numpy ndarray Needed to learn the empirical distribuion *ess* : an integer Equivalent sample size *ed* : an EmpiricalDistribution object Used to cache multiple lookups in structure learning. Notes ----- *a_ijk* : a vector The number of times where x_i=k | parents(x_i)=j -> i.e. the mle counts *a_ij* : a vector summed over k's in a_ijk *n_ijk* : a vector prior (sample size or calculation) ess/(card(x_i)*len(cpt(x_i)/card(x_i))) for x_i for BDe metric *n_ij* : a vector prior summed over k's in n_ijk """ counts_dict = mle_fast(bn, data, counts=True, np=True) a_ijk = [] bdeu = 1 for rv, value in counts_dict.items(): nijk = value['cpt'] nijk_prime = ess / len(nijk) k2 *= gamma(nijk+nijk_prime)/gamma(nijk_prime) nij_prime = nijk_prime*(len(cpt)/bn.card(rv)) nij = np.mean(nijk.reshape(-1, bn.card(rv)), axis=1) # sum along parents k2 *= gamma(nij_prime) / gamma(nij+nij_prime) return bdeu
def K2(bn, data, ed=None): """ K2 is bayesian posterior probability of structure given the data, where N'ijk = 1. """ counts_dict = mle_fast(bn, data, counts=True, np=True) a_ijk = [] k2 = 1 for rv, value in counts_dict.items(): nijk = value['cpt'] nijk_prime = 1 k2 *= gamma(nijk+nijk_prime)/gamma(nijk_prime) nij_prime = nijk_prime*(len(cpt)/bn.card(rv)) nij = np.mean(nijk.reshape(-1, bn.card(rv)), axis=1) # sum along parents k2 *= gamma(nij_prime) / gamma(nij+nij_prime) return k2
def K2(bn, data, ed=None):
"""
K2 is bayesian posterior probability of structure given the data,
where N'ijk = 1.
"""
counts_dict = mle_fast(bn, data, counts=True, np=True)
a_ijk = []
k2 = 1
for rv, value in counts_dict.items():
nijk = value['cpt']
nijk_prime = 1
k2 *= gamma(nijk + nijk_prime) / gamma(nijk_prime)
nij_prime = nijk_prime * (len(cpt) / bn.card(rv))
nij = np.mean(nijk.reshape(-1, bn.card(rv)),
axis=1) # sum along parents
k2 *= gamma(nij_prime) / gamma(nij + nij_prime)
return k2