def updateThetaAndThetaRem(
SS=None, K=None, NodeStateCount=None, rho=None,
alpha=1.0, gamma=10.0):
''' Update parameters theta to maximize objective given suff stats.
Returns
---------
theta : 2D array, nNodes x K
thetaRem : scalar
'''
if K is None:
K = SS.K
if NodeStateCount is None:
NodeStateCount = SS.NodeStateCount
nNodes = NodeStateCount.shape[0]
if rho is None or rho.size != K:
rho = OptimizerRhoOmegaBetter.make_initrho(K, nNodes, gamma)
# Calculate E_q[alpha * Beta_l] for l = 1, ..., K+1
Ebeta = StickBreakUtil.rho2beta(rho, returnSize='K')
alphaEbeta = alpha * Ebeta
alphaEbetaRem = alpha * (1- Ebeta.sum())
theta = alphaEbeta + NodeStateCount
thetaRem = alphaEbetaRem
return theta, thetaRem
def _calcTheta(self, SS):
''' Update parameters theta to maximize objective given suff stats.
Returns
---------
transTheta : 2D array, size K x K+1
startTheta : 1D array, size K
'''
K = SS.K
if not hasattr(self, 'rho') or self.rho.size != K:
self.rho = OptimizerRhoOmega.create_initrho(K)
# Calculate E_q[alpha * Beta_l] for l = 1, ..., K+1
Ebeta = StickBreakUtil.rho2beta(self.rho)
alphaEBeta = self.transAlpha * Ebeta
# transTheta_kl = M_kl + E_q[alpha * Beta_l] + kappa * 1_{k==l}
transTheta = np.zeros((K, K + 1))
transTheta += alphaEBeta[np.newaxis, :]
transTheta[:K, :K] += SS.TransStateCount + self.kappa * np.eye(self.K)
# startTheta_k = r_1k + E_q[alpha * Beta_l] (where r_1,>K = 0)
startTheta = self.startAlpha * Ebeta
startTheta[:K] += SS.StartStateCount
return transTheta, startTheta
def calcHardMergeGap(self, SS, kA, kB):
''' Calculate scalar improvement in ELBO for hard merge of comps kA, kB
Does *not* include any entropy.
Returns
---------
L : scalar
'''
m_K = SS.K - 1
m_SS = SuffStatBag(K=SS.K, D=0)
m_SS.setField('StartStateCount', SS.StartStateCount.copy(), dims='K')
m_SS.setField('TransStateCount',
SS.TransStateCount.copy(),
dims=('K', 'K'))
m_SS.mergeComps(kA, kB)
# Create candidate beta vector
m_beta = StickBreakUtil.rho2beta(self.rho)
m_beta[kA] += m_beta[kB]
m_beta = np.delete(m_beta, kB, axis=0)
# Create candidate rho and omega vectors
m_rho = StickBreakUtil.beta2rho(m_beta, m_K)
m_omega = np.delete(self.omega, kB)
# Create candidate startTheta
m_startTheta = self.startAlpha * m_beta.copy()
m_startTheta[:m_K] += m_SS.StartStateCount
# Create candidate transTheta
m_transTheta = self.alpha * np.tile(m_beta, (m_K, 1))
if self.kappa > 0:
m_transTheta[:, :m_K] += self.kappa * np.eye(m_K)
m_transTheta[:, :m_K] += m_SS.TransStateCount
# Evaluate objective func. for both candidate and current model
Lcur = calcELBO_LinearTerms(SS=SS,
rho=self.rho,
omega=self.omega,
startTheta=self.startTheta,
transTheta=self.transTheta,
alpha=self.alpha,
startAlpha=self.startAlpha,
gamma=self.gamma,
kappa=self.kappa)
Lprop = calcELBO_LinearTerms(SS=m_SS,
rho=m_rho,
omega=m_omega,
startTheta=m_startTheta,
transTheta=m_transTheta,
alpha=self.alpha,
startAlpha=self.startAlpha,
gamma=self.gamma,
kappa=self.kappa)
# Note: This gap relies on fact that all nonlinear terms are entropies,
return Lprop - Lcur
def L_slack(self, SS):
''' Compute slack term of the allocation objective function.
Returns
-------
L : scalar float
'''
ElogPi, ElogPiRem = self.E_logPi(returnRem=1)
Ebeta = StickBreakUtil.rho2beta(self.rho, returnSize='K')
Q = SS.NodeStateCount + self.alpha * Ebeta - self.theta
Lslack = np.sum(Q * ElogPi)
alphaEbetaRem = self.alpha * (1.0 - Ebeta.sum())
LslackRem = np.sum((alphaEbetaRem - self.thetaRem) * ElogPiRem)
return Lslack + LslackRem