def compute_log_posteriors_multisubject(Xs, partitions=None, alpha=None, prior_H=None, verbose=False):
"""Compute log of p(H|Xs) for all the Hs, i.e. the partitions, of
the classes, given the list of confusion matrices Xs for different
(independent subjects), the Dirichlet prior alpha and the
hypotheses' prior p(H) (prior_H).
"""
if partitions is None:
partitions = list(Partition(range(Xs[0].shape[0])))
if alpha is None:
if verbose: print "Assuming non-informative Dirichlet prior."
alpha = np.ones(Xs[0].shape)
if prior_H is None:
if verbose: print "Assuming uniform prior for p(H_i)."
prior_H = np.ones(len(partitions)) / len(partitions)
logp_X_given_H = np.zeros((len(partitions), len(Xs)))
for i, partition in enumerate(partitions):
for j in range(len(Xs)):
logp_X_given_H[i,j] = compute_logp_H(Xs[j], partition, alpha=alpha)
# normalization constant: p(X)
logp_X = reduce(np.logaddexp, logp_X_given_H.sum(1) + np.log(prior_H))
# p(H|X) from Bayes rule:
log_posterior_H_given_X = logp_X_given_H.sum(1) + np.log(prior_H) - logp_X
return log_posterior_H_given_X, partitions
from partitioner import Partition
if __name__ == '__main__':
X = tu
print "X:"
print X
partitions = list(Partition(range(X.shape[0])))
alpha = np.ones(X.shape) # uniform prior on confusion matrices
print "alpha:"
print alpha
# uniform prior on hypotheses: p(H_i)
prior_H = np.ones(len(partitions)) / len(partitions)
logp_X_given_H = np.zeros(len(partitions))
for i, partition in enumerate(partitions):
logp_X_given_H[i] = compute_logp_H(X, partition, alpha=alpha)
# normalization constant: p(X)
logp_X = reduce(np.logaddexp, logp_X_given_H + np.log(prior_H))
# p(H|X) from Bayes rule:
log_posterior_H_given_X = logp_X_given_H + np.log(prior_H) - logp_X
idx = np.argsort(log_posterior_H_given_X)[::-1]
print
for k, i in enumerate(idx[:5]):
print "%s) p(%s | X) = %s" % (k+1, partitions[i], np.exp(log_posterior_H_given_X[i]))
psi = [[0, 1], [2]]
# psi = [[0],[1],[2]]
# psi = [[0],[1,2]]
# psi = [[0,1,2]]
# psi = [[0],[1],[2],[3],[4]]
# psi = [[0,1],[2],[3],[4]]
# psi = [[0,1,2],[3],[4]]
# psi = [[0,1,2,3],[4]]
# psi = [[0,1,2],[3,4]]
# psi = [[0,1,2,3,4]]
print "psi:", psi
alpha = np.ones(X.shape)
print "alpha:"
print alpha
logp_Hs = []
print "psi \t log-likelihood"
partitions = Partition(range(X.shape[0]))
partitions1 = Partition(range(1, X.shape[0] + 1))
for psi in partitions:
logp_H = compute_logp_H(X, psi, alpha)
print psi, logp_H
logp_Hs.append(logp_H)
idxs = np.argsort(logp_Hs)
print
for idx in idxs:
print partitions[idx], logp_Hs[idx]
