def E_step(self, Data, LocalP ):
GroupIDs = Data['GroupIDs']
X = Data['X']
N,D = X.shape
assert self.D == D
# Create lpr : N x K matrix
# where lpr[n,k] =def= log r[n,k], as in Bishop PRML eq 10.67
lpr = np.empty( (N, self.K) )
# LIKELIHOOD Terms
for k in range(self.K):
lpr[:,k] = -0.5*self.qObs[k].dF*self.qObs[k].dist_mahalanobis( X ) \
-0.5*D/self.qObs[k].kappa
lpr += 0.5*self.logdetLam
# PRIOR Terms
for gg in xrange( len(GroupIDs) ):
lpr[ GroupIDs[gg] ] += LocalP['Elogw_perGroup'][gg]
lprSUM = logsumexp(lpr, axis=1)
resp = np.exp(lpr - lprSUM[:, np.newaxis])
resp /= resp.sum( axis=1)[:,np.newaxis] # row normalize
return resp
def E_step(self, Data, LocalP):
GroupIDs = Data['GroupIDs']
X = Data['X']
N, D = X.shape
assert self.D == D
# Create lpr : N x K matrix
# where lpr[n,k] =def= log r[n,k], as in Bishop PRML eq 10.67
lpr = np.empty((N, self.K))
# LIKELIHOOD Terms
for k in range(self.K):
lpr[:,k] = -0.5*self.qObs[k].dF*self.qObs[k].dist_mahalanobis( X ) \
-0.5*D/self.qObs[k].kappa
lpr += 0.5 * self.logdetLam
# PRIOR Terms
for gg in xrange(len(GroupIDs)):
lpr[GroupIDs[gg]] += LocalP['Elogw_perGroup'][gg]
lprSUM = logsumexp(lpr, axis=1)
resp = np.exp(lpr - lprSUM[:, np.newaxis])
resp /= resp.sum(axis=1)[:, np.newaxis] # row normalize
return resp
def E_step( self, X):
lpr = np.log( self.gmm.w ) + self.gmm.calc_soft_evidence_mat( X )
lprPerItem = logsumexp( lpr, axis=1 )
resp = np.exp( lpr-lprPerItem[:,np.newaxis] )
if self.doVerify:
if not np.allclose( np.sum(resp,axis=1), 1.0 ):
np.set_printoptions( linewidth=120, precision=3, suppress=True )
raise Exception, 'Responsibilities do not sum to one!'
logEvidence = lprPerItem.sum()
return resp, logEvidence
def E_step(self, X):
lpr = np.log(self.gmm.w) + self.gmm.calc_soft_evidence_mat(X)
lprPerItem = logsumexp(lpr, axis=1)
resp = np.exp(lpr - lprPerItem[:, np.newaxis])
if self.doVerify:
if not np.allclose(np.sum(resp, axis=1), 1.0):
np.set_printoptions(linewidth=120, precision=3, suppress=True)
raise Exception, 'Responsibilities do not sum to one!'
logEvidence = lprPerItem.sum()
return resp, logEvidence
def E_step(self, Xchunk):
'''Expectation step
Returns
-------
resp : NxK matrix, resp[n,k] = Pr(Z[n]=k | X[n],mu[k],Sigma[k])
'''
lpr = np.log(self.gmm.w) + self.gmm.calc_soft_evidence_mat(Xchunk)
lprPerItem = logsumexp(lpr, axis=1)
logEvidence = lprPerItem.sum()
resp = np.exp(lpr - lprPerItem[:, np.newaxis])
return resp, logEvidence
def E_step( self, Xchunk ):
'''Expectation step
Returns
-------
resp : NxK matrix, resp[n,k] = Pr(Z[n]=k | X[n],mu[k],Sigma[k])
'''
lpr = np.log( self.gmm.w ) + self.gmm.calc_soft_evidence_mat( Xchunk )
lprPerItem = logsumexp(lpr, axis=1)
logEvidence = lprPerItem.sum()
resp = np.exp(lpr - lprPerItem[:, np.newaxis])
return resp, logEvidence
def calc_evidence(self, X):
"""Compute evidence for given data X under current model
Parameters:
X : array_like, N x D
Returns:
evBound : scalar real
= \sum_n log( \sum_k w_k * N( x_n | \mu_k, \sigma_k )
see Bishop PRML eq. 9.28 (p. 439)
"""
lpr = np.log( self.w ) + self.calc_soft_evidence_mat( X )
evidenceBound = logsumexp(lpr, axis=1).sum()
return evidenceBound
def calc_posterior_prob_mat(self, X):
"""Compute posterior probability for hidden component assignment Z
under current model parameters mu,sigma given data X
Parameters:
X : array_like, N x D
Returns:
resp : N x K
= Pr( z_n = k | x_n, \mu_k, \Sigma_k )
see Bishop PRML eq. 9.23 (p. 438)
"""
lpr = np.log( self.w ) + self.calc_soft_evidence_mat( X )
lprSUM = logsumexp(lpr, axis=1)
return np.exp(lpr - lprSUM[:, np.newaxis])
def E_step(self, X):
N, D = X.shape
assert self.D == D
# Create lpr : N x K matrix
# where lpr[n,k] =def= log r[n,k], as in Bishop PRML eq 10.67
lpr = np.empty((N, self.K))
for k in range(self.K):
# calculate the ( x_n - m )'*W*(x_n-m) term
lpr[:,k] = -0.5*self.qObs[k].dF*self.qObs[k].dist_mahalanobis( X ) \
-0.5*D/self.qObs[k].kappa
lpr += self.Elogw
lpr += 0.5 * self.logdetLam
lprSUM = logsumexp(lpr, axis=1)
resp = np.exp(lpr - lprSUM[:, np.newaxis])
resp /= resp.sum(axis=1)[:, np.newaxis] # row normalize
return resp
def E_step(self, X):
N,D = X.shape
assert self.D == D
# Create lpr : N x K matrix
# where lpr[n,k] =def= log r[n,k], as in Bishop PRML eq 10.67
lpr = np.empty( (N, self.K) )
for k in range(self.K):
# calculate the ( x_n - m )'*W*(x_n-m) term
lpr[:,k] = -0.5*self.qObs[k].dF*self.qObs[k].dist_mahalanobis( X ) \
-0.5*D/self.qObs[k].kappa
lpr += self.Elogw
lpr += 0.5*self.logdetLam
lprSUM = logsumexp(lpr, axis=1)
resp = np.exp(lpr - lprSUM[:, np.newaxis])
resp /= resp.sum( axis=1)[:,np.newaxis] # row normalize
return resp