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sample_theta.py
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def sample_theta(theta,Ustats,obsModel,Kextra):
prior_params = obsModel['params']
if obsModel['type']=='Multinomial':
p = theta['p']
store_counts = Ustats['card']
alpha_vec = prior_params['alpha']
Kz,Ks = store_counts.shape
for kz in range(0,Kz):
for ks in range(0,Ks):
#doublecheck
p[kz,ks,:] = randdirichlet([alpha_vec.T+store_counts[:,kz,ks]]).T
theta['p'] = p
elif obsModel['type'] in ['Gaussian','AR','SLDS']:
theta = sample_theta_submodule(theta,Ustats,obsModel['priorType'],prior_params,Kextra)
if obsModel['type']=='SLDS':
y_prior_params = obsModel['y_params']
#doublecheck
theta['theta_r'] = sample_theta_submodule(theta['theta_r'],Ustats['Ustats_r'],\
obsModel['y_priorType'],y_prior_params,[])
return theta
def sample_theta_submodule(theta,Ustats,priorType,prior_params,Kextra):
nu = prior_params['nu']
nu_delta = prior_params['nu_delta']
store_card = Ustats['card']
if store_card.shape[0]==1:
store_card = store_card.T
#double check this is hstack or vstack
store_card = np.vstack((store_card,np.zeros([Kextra,store_card.shape[1]])))
Kz,Ks = store_card.shape
if priorType=='MNIW':
invSigma = theta['invSigma']
A = theta['A']
store_XX = Ustats['XX']
store_YX = Ustats['YX']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
store_sumX = Ustats['sumX']
K = prior_params['K']
M = prior_params['M']
MK = prior_params['M']*prior_params['K']
MKM = MK*prior_params['M'].T
for kz in range(0,Kz):
for ks in range(0,Ks):
if store_card[kz,ks]>0:
# Given X, Y get sufficient statistics
Sxx = store_XX[:,:,kz,ks] + K
Syx = store_YX[:,:,kz,ks] + MK
Syy = store_YY[:,:,kz,ks] + MKM
SyxSxxInv = Syx/Sxx
Sygx = Syy - SyxSxxInv*Syx.T
Sygx = (Sygx + Sygx.T)/2
else:
Sxx = K
SyxSxxInv = M
Sygx = 0
# Sample Sigma given s.stats
sqrtSigma,sqrtinvSigma = randiwishart(Sygx + nu_delta,nu+store_card[kz,ks])
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma
# Sample A given Sigma and s.stats
cholinvSxx = np.linalg.cholesky(np.linalg.inv(Sxx))
A[:,:,kz,ks] = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx)
theta['invSigma'] = invSigma
theta['A'] = A
elif priorType=='NIW':
invSigma = theta['invSigma']
mu = theta['mu']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
K = prior_params['K']
M = prior_params['M']
MK = prior_params['M']*prior_params['K']
MKM = MK*prior_params['M'].T
for kz in range(0,Kz):
for ks in range(0,Ks):
if store_card[kz,ks]>0:
## Given X, Y get sufficient statistics
Sxx = store_card[kz,ks] + K
Syx = store_sumY[:,kz,ks] + MK
Syy = store_YY[:,:,kz,ks] + MKM
SyxSxxInv = Syx/Sxx
Sygx = Syy - SyxSxxInv*Syx.T
Sygx = (Sygx + Sygx.T)/2
else:
Sxx = K
SyxSxxInv = M
Sygx = 0
# Sample Sigma given s.stats
sqrtSigma,sqrtinvSigma = randiwishart(Sygx + nu_delta,nu+store_card[kz,ks])
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma
# Sample A given Sigma and s.stats
cholinvSxx = np.linalg.cholesky(np.linalg.inv(Sxx))
mu[:,kz,ks] = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx)
theta['invSigma'] = invSigma
theta['mu'] = mu
elif priorType=='MNIW-N':
invSigma = theta['invSigma']
A = theta['A']
mu = theta['mu']
store_XX = Ustats['XX']
store_YX = Ustats['YX']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
store_sumX = Ustats['sumX']
# If MNIW-N, K and M are as in MNIW. If IW-N, K=1 and M=0.
K = prior_params['K']
M = prior_params['M']
MK = prior_params['M']*prior_params['K']
MKM = MK*prior_params['M'].T
if 'numIter' not in prior_params.keys():
prior_params.numIter = 50
numIter = prior_params['numIter']
mu0 = prior_params['mu0']
cholSigma0 = prior_params['cholSigma0']
Lambda0 = np.linalg.inv(prior_params['cholSigma0'].T*prior_params['cholSigma0'])
theta0 = Lambda0*prior_params['mu0']
dimu = nu_delta.shape[0]
for kz in range(0,Kz):
for ks in range(0,Ks):
if store_card[kz,ks]>0: #**
for n in range(0,numIter):
## Given X, Y get sufficient statistics
Sxx = store_XX[:,:,kz,ks] + K
Syx = store_YX[:,:,kz,ks] + MK - mu[:,kz,ks]*store_sumX[:,kz,ks].T
Syy = store_YY[:,:,kz,ks] + MKM \
- mu[:,kz,ks]*store_sumY[:,kz,ks].T - store_sumY[:,kz,ks]*mu[:,kz,ks].T + \
store_card[kz,ks]*mu[:,kz,ks]*mu[:,kz,ks].T
SyxSxxInv = Syx/Sxx
Sygx = Syy - SyxSxxInv*Syx.T
Sygx = (Sygx + Sygx.T)/2
# Sample Sigma given s.stats
sqrtSigma,sqrtinvSigma = randiwishart(Sygx + nu_delta,nu+store_card[kz,ks])
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma
# Sample A given Sigma and s.stats
cholinvSxx = np.linalg.chol(np.linalg.inverse(Sxx))
A[:,:,kz,ks] = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx)
# Sample mu given A and Sigma
Sigma_n = inv(Lambda0 + store_card(kz,ks)*invSigma[:,:,kz,ks])
mu_n = Sigma_n*(theta0 + invSigma[:,:,kz,ks]*(store_sumY[:,kz,ks]-A[:,:,kz,ks]\
*store_sumX[:,kz,ks]))
#doublecheck
mu[:,kz,ks] = mu_n + np.linalg.cholesky(Sigma_n).T*np.random.standard_normal(dimu,1)
else:
Sxx = K
SyxSxxInv = M
Sygx = 0
sqrtSigma,sqrtinvSigma = randiwishart(nu_delta,nu)
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma
cholinvK = np.linalg.cholesky(np.linalg.inv(K))
A[:,:,kz,ks] = sampleFromMatrixNormal(M,sqrtSigma,cholinvK)
mu[:,kz,ks] = mu0 + cholSigma0.T*np.random.standard_normal((dimu,1))
theta['invSigma'] = invSigma
theta['A'] = A
theta['mu'] = mu
elif priorType=='IW-N':
invSigma = theta['invSigma']
mu = theta['mu']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
if 'numIter' not in prior_params.keys():
prior_params['numIter'] = 50
numIter = prior_params['numIter']
mu0 = prior_params['mu0']
cholSigma0 = prior_params['cholSigma0']
Lambda0 = np.linalg.inv(prior_params['cholSigma0'].T*prior_params['cholSigma0'])
theta0 = Lambda0*prior_params['mu0']
dimu = nu_delta.shape[0]
for kz in range(0,Kz):
for ks in range(0,Ks):
if store_card[kz,ks]>0: #**
for n in range(0,numIter):
## Given X, Y get sufficient statistics
Syy = store_YY[:,:,kz,ks] + \
- mu[:,kz,ks]*store_sumY[:,kz,ks].T - store_sumY[:,kz,ks]*mu[:,kz,ks].T +\
store_card[kz,ks]*mu[:,kz,ks]*mu[:,kz,ks].T
Sygx = (Syy + Syy.T)/2
# Sample Sigma given s.stats
sqrtSigma,sqrtinvSigma = randiwishart(Sygx + nu_delta,nu+store_card[kz,ks])
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma;
# Sample A given Sigma and s.stats
cholinvSxx = np.linalg.cholesky(np.linalg.inv(Sxx))
A[:,:,kz,ks] = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx)
# Sample mu given A and Sigma
Sigma_n = np.linalg.inv(Lambda0 + store_card[kz,ks]*invSigma[:,:,kz,ks])
mu_n = Sigma_n*(theta0 + invSigma[:,:,kz,ks]*store_sumY[:,kz,ks])
mu[:,kz,ks] = mu_n + np.linalg.cholesky(Sigma_n).T*np.random.standard_normal((dimu,1))
else:
sqrtSigma,sqrtinvSigma = randiwishart(nu_delta,nu)
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma
mu[:,kz,ks] = mu0 + cholSigma0.T*np.random.standard_normal(dimu,1)
theta['invSigma'] = invSigma
theta['A'] = A
theta['mu'] = mu
elif priorType=='IW-N-tiedwithin':
invSigma = theta['invSigma']
mu = theta['mu']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
if 'numIter' not in prior_params.keys():
prior_params['numIter'] = 50
numIter = prior_params['numIter']
mu0 = prior_params['mu0']
cholSigma0 = prior_params['cholSigma0']
Lambda0 = np.linalg.inv(prior_params['cholSigma0'].T*prior_params['cholSigma0'])
theta0 = Lambda0*prior_params['mu0']
dimu=nu_delta.shape[0]
for kz in range(0,numIter):
store_invSigma = invSigma[:,:,kz,1]
for n in range(0,numIter):
for ks in range(0,Ks):
if store_card(kz,ks)>0:
Sigma_n = np.linalg.inv(Lambda0 + store_card[kz,ks]*store_invSigma)
mu_n = Sigma_n*(theta0 + store_invSigma*store_sumY[:,kz,ks])
mu[:,kz,ks] = mu_n + np.linalg.cholesky(Sigma_n).T*np.random.standard_normal((dimu,1))
else:
mu[:,kz,ks] = mu0 + cholSimga0.T*np.random.standard_normal((dimu,1))
#Given Y get sufficient statistics
store_card_kz = store_card[kz,:]
#need to double check squeeze function
squeeze_mu_kz = squeeze(mu[:,kz,:])
muY = squeeze_mu_kz*squeeze(store_sumY[:,kz,:].T)
muN = (np.matlib.repmat(store_card_kz,(dimu,1))*squeeze_mu_kz)*squeeze_mu_kz.T
Syy = np.sum(store_YY[:,:,kz,:],axis=3) - muY - muY.T+muN
Syy = (Syy+Syy.T)/2
# Sample Sigma given s.stats
sqrtSigma,sqrtinvSigma = randiwishart(Syy+nu_delta,nu+np.sum(store_card_kz))
store_invSigma = sqrtSigma.T*sqrtSigma
invSigma[:,:,kz,0:Ks]=np.matlib.repmat(store_invSigma,np.array([1,1,1,Ks]))
theta['invSigma'] = invSigma
theta['mu'] = mu
elif priorType in ['N-IW-N','Afixed-IW-N','ARD']:
invSigma = theta['invSigma']
A = theta['A']
mu = theta['mu']
store_XX = Ustats['XX']
store_YX = Ustats['YX']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
store_sumX = Ustats['sumX']
if 'numIter' not in prio_params.keys():
prior_params['numIter']=50
numIter = prior_params['numIter']
if 'zeroMean' in prior_params.keys():
mu0 = prior_params['mu0']
cholSigma0 = prior_params['cholSigma0']
Lambda0 = np.linalg.inv(prior_params['cholSigma0'].T*prior_params['cholSigma0'])
theta0 = Lambda0*prior_params['mu0']
r = A.shape[1]/A.shape[0]
if priorType=='N-IW-N':
M = prior_params['M']
Lambda0_A = prior_params['Lambda0_A']
theta0_A = Lambda0_A*M[:]
dim_vecA = M.size
XinvSigmaX = np.zeros((dim_vecA,dim_vecA))
XinvSigmay = np.zeros((dim_vecA,1))
elif priorType=='ARD':
M=np.zeros(A[:,:,1,1].shape)
theta0_A = np.zeros((A.size,1))
dim_vecA = M.size
a_ARD = prior_params['a_ARD']
b_ARD = prior_params['b_ARD']
if r==1:
numHypers = M.shape[0]
else:
numHypers =r
ARDhypers = np.ones((numHypers,Kz,Ks))
posInds = np.where(store_card>0)
if x.size>0:
ARDhypers[:,0:mu.shape[1]]=theta['ARDhypers']
dim = nu_delta.shape[0]
for n in range(0,numIter):
for kz in range(0,Kz):
for ks in range(0,Ks):
if store_card[kz,ks]>0:
#Sample Sigma given A, mu, and s.stats
S= store_YY[:,:,kz,ks] + A[:,:,kz,ks]*store_XX[:,:,kz,ks]*A[:,:,kz,ks].T\
-A[:,:,kz,ks]*store_YX[:,:,kz,ks].T - store_YX[:,:,kz,ks]*A[:,:,kz,ks].T\
-mu[:,kz,ks]*(store_sumY[:,kz,ks]-A[:,:,kz,ks]*store_sumX[:,kz,ks]).T-\
(store_sumY[:,kz,ks]-A[:,:,kz,ks]*store_sumX[:,kz,ks])*mu[:,kz,ks].T\
+store_card[kz,ks]*mu[:,kz,ks]*mu[:,kz,ks].T
S=0.5*(S+S.T)
sqrtSigma,sqrtinvSigma=randiwishart(S+nu_delta,nu+store_card[kz,ks])
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma
if prior_params=='zeroMean':
mu[:,kz,ks]=np.zeros((dimu,1))
else:
#Sample mu given A, Sigma, and s.stats
Sigma_n = np.inv(Lambda0 + store_card(kz,ks)*invSigma[:,:,:kz,ks])
mu_n = Sigma_n *(theta0 + invSigma[:,:,kz,ks]*(store_sumY[:,kz,ks]-A[:,:,kz,ks]*store_sumX[:,kz,ks]))
mu[:,kz,ks] = mu_n +np.cholesky(Sigma_n).T*randn(dimu,1)
if priorType='N-IW-N':
XinvSigmaX=XinvSigmaX+np.kron(store_XX[:,:,kz,ks],invSigma[:,:,kz,ks])
temp = invSigma[:,:,kz,ks]*(store_YX[:,:,kz,ks]-mu[:,kz,ks]*store_sumX[:,kz,ks].T)
XinvSigmay = XinvSigmay + temp[:] #since A is shared, grow for all data, not just kz,ks
elif priorType=='ARD':
XinvSigmaX = np.kron(store_XX[:,:,kz,ks],invSigma[:,:,kz,ks])
XinvSigmay = invSigma[:,:,kz,ks]*(store_YX[:,:,kz,ks]-mu[:,kz,ks]*store_sumX[:,kz,ks].T)
XinvSigmay = XinvSigmay[:]
ARDhypers_kzks = ARDhypers[:,kz,ks]
if r == 1:
numObsPerHyper = numRow
else:
numObsPerHyper = numRow*(numCol/r)
ARDhypers_kzks = ARDhypers_kzks[:,np.ones([1,numObsPerHyper])].T
ARDhypers_kzks = ARDhypers_kzks[:]
Lambda0_A = np.diag(ARDhypers_kzks)
Sigma_A = np.linalgo.inv(Lambda0_A + XinvSigmaX)
mu_A = Sigma_A*(theta0_A + XinvSigmay)
vecA = mu_A + np.linalg.cholesky(Sigma_A).T*randn(dim_vecA,1)
#A(:,:,kz,ks) = reshape(vecA,size(M))
#AA = sum(A(:,:,kz,ks).*A(:,:,kz,ks),1);
#if r>1:
# AA = reshape(AA,[numCol/r r]);
# AA = sum(AA,1);
aa = np.zeros([1,numHypers])
for ii in range(0,numHypers):
aa(ii) = randgamma(a_ARD + numObsPerHyper/2);
#aa(ii) = randgamma(a_ARD + numRow/2);
ARDhypers[:,kz,ks] = aa / (b_ARD + AA/2);
elif priorType=='IW':
invSigma = theta['invSigma']
store_YY = Ustats['YY']
store_sumY = Ustats['sumY']
dimu = np.shape(nu_delta)[0]
for kz in range(0,Kz):
for ks in range(0,Ks):
if store_card[kz,ks]>0: #**
# Given X, Y get sufficient statistics
Syy = store_YY[:,:,kz,ks]
Sygx = (Syy + Syy.T)/2
# Sample Sigma given s.stats
sqrtSigma,sqrtinvSigma = randiwishart(Sygx + nu_delta,nu+store_card[kz,ks])
invSigma(:,:,kz,ks) = sqrtinvSigma.T*sqrtinvSigma
else:
sqrtSigma,sqrtinvSigma = randiwishart(nu_delta,nu);
invSigma[:,:,kz,ks] = sqrtinvSigma.T*sqrtinvSigma;
theta['invSigma'] = invSigma
return theta