def optO(xs,E,T_prior,beta,L,NHW):
#format: lambda xs,Z0: optOMult(xs,Z0,NW)
#1. convert xs (time/space observations) to X,D
ls = zip(*xs)[0]
ds = zip(*xs)[2]
X = array([arrayWithOne(l,L) for l in ls])
D = array([arrayWithOne(d,NHW) for d in ds])
#since E is Nx2, we can take just the second column to provide the same info (and this is what the opt functions expect)
return {'mu':optT(X, E[:,1], T_prior), 'omega':optQ(D, E[:,1], X, NHW, beta)}
def logOptOMult(xs,Z0,NW):
#MAP approach (with prior pseudo count 0.5)
alpha = 0.0 # 0.5
N = len(xs)
(N1,K) = shape(Z0)
assert N==N1,'%i %i'%(N,N1)
#convert xs to matrix X:
X0 = zeros((N,NW))
for n in range(N): X0[n,:] = arrayWithOne(xs[n],NW)
#for each word w in NW, calcualate frequency
lgF = log(zeros( (NW,K) ) + alpha)
for k in range(K):
Zsum = Z0[:,k].sum()
if Zsum>0:
for w in range(NW):
log_xz_sum = -inf
for n in range(N):
log_xz_sum = logaddexp(log_xz_sum, log(X0[n,w]) + log(Z0[n,k]))
lgF[w,k] = log_xz_sum-log(Zsum + NW*alpha)
#make sure normalized:
assert all( abs(exp(lgF).sum(axis=0)-1.) < 1e-4), exp(lgF).sum(axis=0)
#make sure no zero entries (otherwise we get into trouble with testing when an obs with zero probability happens)
#assert all(lgF>-inf),lgF.T
return lgF.T
def optOMult(xs,Z0,NW):
#MAP approach (with prior pseudo count 0.5
alpha = 0.5
N = len(xs)
(N1,K) = shape(Z0)
assert N==N1
#convert xs to matrix X:
X0 = zeros((N,NW))
for n in range(N): X0[n,:] = arrayWithOne(xs[n],NW)
#for each word w in NW, calcualate frequency
F = zeros( (NW,K) ) + alpha
for k in range(K):
Zsum = Z0[:,k].sum()
for w in range(NW):
F[w,k] += (X0[:,w]*Z0[:,k]).sum()
F[w,k] /= (Zsum+NW*alpha)
#print 'F',F
#normalise:
#O = F/reshape(F.sum(axis=1),(K,1))
#make sure no zero entries (otherwise we get into trouble with testing when an obs with zero probability happens)
assert all(F>0),F.T
assert all((F.sum(axis=0)-1.0) < 0.000001),F.T
return F.T