def mhmm_logprob(data, prior, transmat, mu, Sigma, mixmat=None):
'''
% LOG_LIK_MHMM Compute the log-likelihood of a dataset using a (mixture of) Gaussians HMM
% [loglik, errors] = log_lik_mhmm(data, prior, transmat, mu, sigma, mixmat)
%
% data{m}(:,t) or data(:,t,m) if all cases have same length
% errors is a list of the cases which received a loglik of -infinity
%
% Set mixmat to ones(Q,1) or omit it if there is only 1 mixture component
'''
Q = len(prior);
if mixmat.shape[0] != Q: # trap old syntax
raise Exception, 'mixmat should be QxM'
if mixmat==None:
mixmat = np.ones((Q,1))
if not isinstance(data, list):
data = [data[:,:,i] for i in range(data.shape[2])]
ncases = len(data);
loglik = 0
errors = []
for m in range(ncases):
obslik, _ = mixgauss_prob(data[m], mu, Sigma, mixmat);
alpha, beta, gamma, ll, _, _ = fwdback(prior, transmat, obslik, fwd_only=True)
if ll==-np.Inf:
errors.append(m)
loglik = loglik + ll
return loglik, errors
def test_1D_M2_Spherical(self):
m = np.array([[1, 2]])
C = 1
x = np.matrix([1])
B, B2 = mixgauss_prob(x, m, C)
assert np.all(np.abs(B==np.matrix([[0.3989],[0.2420]])) < 1e-3)
assert np.all(np.abs(B2==np.array([[[0.3989]],[[0.2420]]])) < 1e-3)
def test_1D_M1_Spherical(self):
m = np.matrix([1])
C = 1
x = np.matrix([1])
B, B2 = mixgauss_prob(x, m, C)
assert np.all(np.abs(B==np.matrix([[0.3989]])) < 1e-3)
assert np.all(np.abs(B2==np.matrix([[0.3989]])) < 1e-3)
def test2D_M2_tied_ind_MQ(self):
m = np.matrix([[1], [2]])
C = np.matrix([[1, 0], [0, 1]])
x = np.matrix([[1], [2]])
B, B2 = mixgauss_prob(x, m, C)
assert np.all(np.abs(B == np.matrix([[0.1592]])) < 1e-3)
assert np.all(np.abs(B2 == np.matrix([[0.1592]])) < 1e-3)
def test_1D_M2_Spherical(self):
m = np.array([[1, 2]])
C = 1
x = np.matrix([1])
B, B2 = mixgauss_prob(x, m, C)
assert np.all(np.abs(B == np.matrix([[0.3989], [0.2420]])) < 1e-3)
assert np.all(np.abs(B2 == np.array([[[0.3989]], [[0.2420]]])) < 1e-3)
def test_1D_M1_Spherical(self):
m = np.matrix([1])
C = 1
x = np.matrix([1])
B, B2 = mixgauss_prob(x, m, C)
assert np.all(np.abs(B == np.matrix([[0.3989]])) < 1e-3)
assert np.all(np.abs(B2 == np.matrix([[0.3989]])) < 1e-3)
def test2D_M2_tied_ind_MQ(self):
m = np.matrix([[1],[2]])
C = np.matrix([[1,0],
[0,1]])
x = np.matrix([[1],
[2]])
B, B2 = mixgauss_prob(x, m, C)
assert np.all(np.abs(B==np.matrix([[0.1592]])) < 1e-3)
assert np.all(np.abs(B2==np.matrix([[0.1592]])) < 1e-3)
def ess_mhmm(prior, transmat, mixmat, mu, Sigma, data):
'''
% ESS_MHMM Compute the Expected Sufficient Statistics for a MOG Hidden Markov Model.
%
% Outputs:
% exp_num_trans(i,j) = sum_l sum_{t=2}^T Pr(Q(t-1) = i, Q(t) = j| Obs(l))
% exp_num_visits1(i) = sum_l Pr(Q(1)=i | Obs(l))
%
% Let w(i,k,t,l) = P(Q(t)=i, M(t)=k | Obs(l))
% where Obs(l) = Obs(:,:,l) = O_1 .. O_T for sequence l
% Then
% postmix(i,k) = sum_l sum_t w(i,k,t,l) (posterior mixing weights/ responsibilities)
% m(:,i,k) = sum_l sum_t w(i,k,t,l) * Obs(:,t,l)
% ip(i,k) = sum_l sum_t w(i,k,t,l) * Obs(:,t,l)' * Obs(:,t,l)
% op(:,:,i,k) = sum_l sum_t w(i,k,t,l) * Obs(:,t,l) * Obs(:,t,l)'
'''
verbose = False
# [O T numex] = size(data);
numex = len(data)
O = data[0].shape[0]
Q = len(prior)
M = mixmat.shape[1]
exp_num_trans = np.zeros((Q, Q));
exp_num_visits1 = np.zeros((Q, 1));
postmix = np.zeros((Q, M));
m = np.zeros((O, Q, M));
op = np.zeros((O, O, Q, M));
ip = np.zeros((Q, M));
mix = M > 1
loglik = 0
if verbose:
print 'forwards-backwards example # '
for ex in range(0, numex):
if verbose:
print '%d ' % ex
# obs = data(:,:,ex);
obs = data[ex]
T = obs.shape[1]
if mix:
B, B2 = mixgauss_prob(obs, mu, Sigma, mixmat)
alpha, beta, gamma, current_loglik, xi_summed, gamma2 = fwdback(prior, transmat, B, obslik2=B2, mixmat=mixmat, compute_xi=True, compute_gamma2=True)
else:
B, B2 = mixgauss_prob(obs, mu, Sigma)
alpha, beta, gamma, current_loglik, xi_summed, _ = fwdback(prior, transmat, B)
loglik = loglik + current_loglik
if verbose:
print 'll at ex %d = %f\n' % (ex, loglik)
exp_num_trans = exp_num_trans + xi_summed # sum(xi,2)
exp_num_visits1 = exp_num_visits1 + gamma[:, 0]
if mix:
postmix = postmix + np.sum(gamma2, 2)
else:
postmix = postmix + np.sum(gamma, 1)
gamma2 = np.reshape(gamma, (Q, 1, T)) # gamma2(i,m,t) = gamma(i,t)
for i in range(0, Q):
for k in range(0, M):
w = np.reshape(gamma2[i, k, :], (1, T)) # w(t) = w(i,k,t,l)
wobs = np.multiply(obs,w) # np.repmat(w, [O 1]) # wobs(:,t) = w(t) * obs(:,t)
m[:, i, k] = m[:, i, k] + np.sum(wobs, 1) # m(:) = sum_t w(t) obs(:,t)
op[:, :, i, k] = op[:, :, i, k] + np.dot(wobs, obs.T) # op(:,:) = sum_t w(t) * obs(:,t) * obs(:,t)'
ip[i, k] = ip[i, k] + np.sum(np.sum(np.multiply(wobs, obs), 1)) # ip = sum_t w(t) * obs(:,t)' * obs(:,t)
if verbose:
print
return loglik, exp_num_trans, np.asarray(exp_num_visits1)[:,0], postmix, m, ip, op