def eA(tau_a0,tau_a1,K):
exp_ln_a = zeros((K,K))
acc = digamma(tau_a0) - digamma(tau_a0 + tau_a1)
for i in range(K):
for j in range(K):
exp_ln_a[i,j] = digamma(tau_a1[i,j]) - digamma(tau_a0[i,j] + tau_a1[i,j]) + acc[i,:j].sum()
return exp_ln_a
def eA(tau_a0,tau_a1,K):
exp_ln_a = np.zeros((K,K))
acc = digamma(tau_a0) - digamma(tau_a0 + tau_a1)
for i in range(K):
for j in range(K):
exp_ln_a[i,j] = digamma(tau_a1[i,j]) - digamma(tau_a0[i,j] + tau_a1[i,j]) + acc[i,:j].sum()
return exp_ln_a
def m(self,X,exp_z):
#given expected value of z, calculate the variational parameters of each component (w.r.t. this sensor)
alpha_c = self._hyperparams['c'] #assumes symmetric prior (though this is v. easy to change to non-symmetric prior)
tau_ctk = alpha_c + dot(X.T, exp_z)
self._tau_ctk = tau_ctk
self._exp_ctk = tau_ctk / tau_ctk.sum(axis=0)
self._exp_ln_ctk = digamma(tau_ctk) - digamma(tau_ctk.sum(axis=0))
def m(self, X, exp_z):
#given expected value of z, calculate the variational parameters of each component (w.r.t. this sensor)
alpha_c = self._hyperparams[
'c'] #assumes symmetric prior (though this is v. easy to change to non-symmetric prior)
tau_ctk = alpha_c + dot(X.T, exp_z)
self._tau_ctk = tau_ctk
self._exp_ctk = tau_ctk / tau_ctk.sum(axis=0)
self._exp_ln_ctk = digamma(tau_ctk) - digamma(tau_ctk.sum(axis=0))
def log_lambda(vk, dim, K, w):
log = np.zeros((K,))
for k in range(K):
(_, log[k]) = slogdet(w[k, :, :])
log[k] += np.sum([digamma((vk[k]+1-i)/2.0) for i in range(dim)])
log += dim*np.log(2.0)
return log #[K,1]
def Invcopt(W,vk,XDim,K):
invc = [None for _ in range(K)]
for k in range(K):
dW = det(W[k])
print 'dW',dW
if dW>1e-30: ld = log(dW)
else: ld = 0.0
invc[k] = sum([digamma((vk[k]+1-i) / 2.) for i in range(XDim)]) + XDim*log(2) + ld
return invc
def _eInvc(self,W,vk,XDim,K):
invc = [None for _ in range(K)]
for k in range(K):
dW = np.linalg.det(W[k])
#print 'dW',dW
if dW>1e-30:
ld = np.log(dW)
else:
ld = 0.0
invc[k] = sum([digamma((vk[k]+1-i) / 2.) for i in range(XDim)]) + XDim*np.log(2) + ld
return np.array(invc)
def Piopt(alpha0,NK):
alphak = alpha0 + NK
pik = digamma(alphak) - digamma(alphak.sum())
return pik
def ePi(tau_pi0,tau_pi1,K):
exp_ln_pi = np.zeros(K)
acc = digamma(tau_pi0) - digamma(tau_pi0 + tau_pi1)
for k in range(K): exp_ln_pi[k] = digamma(tau_pi1[k]) - digamma(tau_pi0[k] + tau_pi1[k]) + acc[:k].sum()
return exp_ln_pi
def log_pi(alphak):
return digamma(alphak) - digamma(alphak.sum()) #[K,]
def ePi(tau_pi0,tau_pi1,K):
exp_ln_pi = zeros(K)
acc = digamma(tau_pi0) - digamma(tau_pi0 + tau_pi1)
for k in range(K): exp_ln_pi[k] = digamma(tau_pi1[k]) - digamma(tau_pi0[k] + tau_pi1[k]) + acc[:k].sum()
return exp_ln_pi
