Skip to content

@emanuele /polya_issue.py
Created

Embed URL

HTTPS clone URL

Subversion checkout URL

You can clone with
or
.
Download ZIP
Issue with multivariate Polya distribution estimation
import numpy as np
from scipy.special import gammaln
def log_multivariate_polya(X, alpha):
N = X.sum()
A = alpha.sum()
log_likelihood = gammaln(N+1) - gammaln(X+1).sum()
log_likelihood += gammaln(A) - gammaln(alpha).sum()
log_likelihood += gammaln(X + alpha).sum() - gammaln(N + A)
return log_likelihood
def logmean(loga):
return reduce(np.logaddexp, loga) - np.log(loga.size)
def log_multivariate_polya_montecarlo(X, alpha, iterations=1e5):
Theta = np.random.dirichlet(alpha, size=int(iterations))
logps = gammaln(X.sum() + 1) - gammaln(X + 1).sum()
logps += (X * np.log(Theta)).sum(1)
return logmean(logps)
if __name__ == '__main__':
np.random.seed(0)
X = np.array([0,50,50])
alpha = np.array([1,10,10])
print "X:", X
print "alpha:", alpha
print "analytic:", log_multivariate_polya(X, alpha)
print "montecarlo", log_multivariate_polya_montecarlo(X, alpha)
print
X = np.array([100,0,0])
alpha = np.array([1,10,10])
print "X:", X
print "alpha:", alpha
print "analytic:", log_multivariate_polya(X, alpha)
print "montecarlo", log_multivariate_polya_montecarlo(X, alpha)
@emanuele
Owner

This is the output if you run this code:


X: [ 0 50 50]
alpha: [ 1 10 10]
analytic: -5.22892710577
montecarlo -5.23470053651

X: [100 0 0]
alpha: [ 1 10 10]
analytic: -51.737395965
montecarlo -93.5266543113


Why there is such a big disagreement between the two implementations in the second case?

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Something went wrong with that request. Please try again.