def incremental_em_hmm(X,
init_pi,
init_obs_distr,
t_min=100,
step=None,
m_step_delta=1,
Xtest=None,
monitor=None):
pi = init_pi.copy()
obs_distr = copy.deepcopy(init_obs_distr)
if step is None:
step = lambda t: 1. / t
T = X.shape[0]
K = len(obs_distr)
A = 1. / K * np.ones((K, K))
seq = np.zeros(T, dtype=int) # online filtering sequence
tau = np.zeros((T, K)) # filter
emissions = np.array([d.pdf(X[0]) for d in obs_distr]).flatten()
phi = pi * emissions # current marginal in q-distribution
phi /= phi.sum()
tau[0] = phi
seq[0] = np.argmax(phi)
s_pairs = distributions.TransitionISufficientStatistics(K)
s_obs = [
d.new_incremental_sufficient_statistics(X[0], phi, i)
for i, d in enumerate(obs_distr)
]
ll_test = []
if Xtest is not None:
lalpha_test, lbeta_test = alpha_beta(Xtest, pi, A, obs_distr)
ll_test.append(log_likelihood(lalpha_test, lbeta_test))
monitor_vals = []
if monitor:
monitor_vals.append(monitor(A, obs_distr))
for t in range(1, T):
# E-step
emissions = np.array([d.pdf(X[t]) for d in obs_distr]).flatten()
q = A * emissions # new q_t transition
q /= q.sum(axis=1)[:, nax]
phi_q = phi[:, nax] * q # for transition statistics
phi = phi_q.sum(axis=0)
# compute filter
tau[t] = emissions * A.T.dot(tau[t - 1])
tau[t] /= tau[t].sum()
seq[t] = np.argmax(tau[t])
# sufficient statistics updates
s = step(t)
s_pairs.online_update(phi_q, s)
for k in range(K):
s_obs[k].online_update(X[t], phi, s)
# M-step
if t < t_min or t % m_step_delta != 0:
continue
# Tracer()()
A = s_pairs.get_statistics()
A /= A.sum(axis=1)[:, nax]
for k in range(K):
obs_distr[k].online_max_likelihood(s_obs[k], t=t)
if Xtest is not None and t % 100 == 0:
lalpha_test, lbeta_test = alpha_beta(Xtest, pi, A, obs_distr)
ll_test.append(log_likelihood(lalpha_test, lbeta_test))
if monitor:
monitor_vals.append(monitor(A, obs_distr))
return seq, tau, A, obs_distr, ll_test, monitor_vals
def incremental_em_hmm_add(X,
lmbda,
alpha=1.5,
Kmax=30,
init_pi=None,
init_obs_distr=None,
dist_cls=distributions.KL,
dist_params=None,
t_min=100,
step=None,
Xtest=None,
monitor=None):
if dist_params is None:
dist_params = {}
if init_obs_distr is None:
obs_distr = [dist_cls(X[0], **dist_params)]
pi = 1.
else:
obs_distr = copy.deepcopy(init_obs_distr)
pi = copy.deepcopy(init_pi)
if step is None:
step = lambda t: 1. / t
T = X.shape[0]
K = 1
A = np.zeros((K, K))
A[0, 0] = 1.
seq = np.zeros(T, dtype=int)
emissions = np.array([d.pdf(X[0]) for d in obs_distr]).flatten()
phi = pi * emissions
phi /= phi.sum()
tau = phi
seq[0] = np.argmax(phi)
s_pairs = distributions.TransitionISufficientStatistics(Kmax)
s_obs = [
d.new_incremental_sufficient_statistics(X[0], phi, i)
for i, d in enumerate(obs_distr)
]
t_init = [0 for _ in range(len(obs_distr))]
ll_test = []
if Xtest is not None:
lalpha_test, lbeta_test = alpha_beta(Xtest,
np.ones(K) / K, A, obs_distr)
ll_test.append(log_likelihood(lalpha_test, lbeta_test))
monitor_vals = []
if monitor:
monitor_vals.append(monitor(A, obs_distr))
for t in range(1, T):
# E-step
new_distr = dist_cls(X[0], **dist_params)
new_distr.max_likelihood(X[t][nax, :], np.ones(1))
emissions = np.array([d.pdf(X[t])
for d in obs_distr + [new_distr]]).flatten()
q = A * emissions[:K]
Z = q.sum(axis=1)
q /= Z[:, nax]
phi_q = phi[:, nax] * q
added_state = False
if K < Kmax: # test new model with K+1 states
Anew = alpha - 1 + s_pairs.get_statistics()[:K, :K + 1]
Anew[np.eye(K) == 1] += 0.5 * alpha
Anew /= Anew.sum(axis=1)[:, nax]
q_new = Anew * emissions
Z_new = q_new.sum(axis=1)
q_new /= Z_new[:, nax]
phi_q_new = phi[:, nax] * q_new
loglik = phi.dot(np.log(Z))
loglik_new = phi.dot(np.log(Z_new))
if loglik_new - lmbda > loglik:
A = Anew
q = q_new
phi_q = phi_q_new
added_state = True
K = K + 1
obs_distr.append(new_distr)
t_init.append(t)
phi = phi_q.sum(axis=0)
# compute filter
tau = emissions[:K] * A.T.dot(tau)
tau /= tau.sum()
seq[t] = np.argmax(tau)
# sufficient statistics updates
s = step(t)
phq = np.zeros((Kmax, Kmax))
phq[:phi_q.shape[0], :phi_q.shape[1]] = phi_q
s_pairs.online_update(phq, s)
for k in range(len(s_obs)):
s_obs[k].online_update(X[t], phi, step(t - t_init[k] + 1))
if added_state:
s_obs.append(
new_distr.new_incremental_sufficient_statistics(
X[t], phi, K - 1))
# M-step
# if t < t_min:
# continue
# Tracer()()
A = alpha - 1 + s_pairs.get_statistics()[:K, :K]
A[np.eye(K) == 1] += 0.5 * alpha
A /= A.sum(axis=1)[:, nax]
for k in range(K):
obs_distr[k].online_max_likelihood(s_obs[k], t=t - t_init[k] + 1)
if Xtest is not None and t % 100 == 0:
lalpha_test, lbeta_test = alpha_beta(Xtest,
np.ones(K) / K, A, obs_distr)
ll_test.append(log_likelihood(lalpha_test, lbeta_test))
if monitor:
monitor_vals.append(monitor(A, obs_distr))
Tracer()()
return seq, A, obs_distr, ll_test, monitor_vals
def incremental_em_hsmm(X, init_pi, init_obs_distr, init_dur_distr, t_min=100, step=None, fit_durations=False):
pi = init_pi.copy()
obs_distr = copy.deepcopy(init_obs_distr)
if fit_durations:
dur_distr = copy.deepcopy(init_dur_distr)
else:
dur_distr = init_dur_distr
D = dur_distr[0].D
if step is None:
step = lambda t: 1. / t
T = X.shape[0]
K = len(obs_distr)
A = 1. / K * np.ones((K,K))
seq = np.zeros(T, dtype=int)
phi = np.zeros((K, D))
tau = np.zeros(K) # tau[i] = sum_d phi(i,d)
emissions = np.array([d.pdf(X[0]) for d in obs_distr]).flatten()
phi[:,0] = pi * emissions
phi[:,0] /= phi[:,0].sum()
tau = phi[:,0]
seq[0] = np.argmax(tau)
# q[i,d,j] = q_t(j,1|i,d) if j > 0
# q[i,d,0] = q_t(i,d+1|i,d)
q = np.zeros((K,D,K+1))
s_pairs = distributions.TransitionISufficientStatistics(K)
s_obs = [d.new_incremental_sufficient_statistics(X[0], tau, i)
for i, d in enumerate(obs_distr)]
if fit_durations:
pass # TODO
# s_dur = [d.new_incremental_sufficient_statistics(i, K, D)
# for i, d in enumerate(dur_distr)]
for t in range(1,T):
## E-step
# d_frac[i,d] = lambda_i(d) = D_i(d+1)/D_i(d)
d_frac = np.vstack(d.d_frac() for d in dur_distr)
emissions = np.array([d.pdf(X[t]) for d in obs_distr]).flatten()
# new q_t[i,j,d] transition
q[:,:,1:] = (1 - d_frac)[:,:,nax] * A[:,nax,:] * emissions[nax,nax,:]
q[:,:,0] = d_frac * emissions[:,nax]
q /= q.sum(2)[:,:,nax]
# phi_q[i,j] = sum_d phi_{t-1}(i,d) q_t(j,1|i,d) (for transitions)
phi_q = np.sum(phi[:,:,nax] * q[:,:,1:], axis=1)
# update phi
# phi_t(j,1)
phi_1 = np.tensordot(phi, q[:,:,1:], axes=2)
phi[:,1:] = phi[:,:-1] * q[:,:-1,0]
phi[:,0] = phi_1
tau = phi.sum(1)
# online sequence estimate (could improve using a filter)
seq[t] = np.argmax(tau)
# sufficient statistics updates
s = step(t)
s_pairs.online_update(phi_q, s)
for k in range(K):
s_obs[k].online_update(X[t], tau, s)
if fit_durations:
pass # TODO
# s_dur[k].online_update(r, r_marginal, s)
## M-step
if t < t_min:
continue
A = s_pairs.get_statistics()
A /= A.sum(axis=1)[:,nax]
for k in range(K):
obs_distr[k].online_max_likelihood(s_obs[k], t=t)
if fit_durations:
pass # TODO
# dur_distr[k].online_max_likelihood(s_dur[k], t=t)
return seq, A, obs_distr, dur_distr