def __init__(self, letter_type, rho=1.0, alpha=1.0, gamma=1.0, lmbda=4.0):
self.letter_dim = letter_type
self.init_dist = InitialState(state_dim=letter_type, rho=rho)
self.letter_trans = WordTransitions(state_dim=letter_type,
alpha=alpha,
gamma=gamma)
self.letter_dur = PoissonDuration(lmbda=lmbda)
class WordModel(object):
def __init__(self, letter_type, rho=1.0, alpha=1.0, gamma=1.0, lmbda=4.0):
self.letter_dim = letter_type
self.init_dist = InitialState(state_dim=letter_type, rho=rho)
self.letter_trans = WordTransitions(state_dim=letter_type,
alpha=alpha,
gamma=gamma)
self.letter_dur = PoissonDuration(lmbda=lmbda)
def resample(self, data):
self.letter_trans.resample(data)
self.init_dist.resample([word[:1] for word in data])
def generate(self):
word_size = self.letter_dur.rvs() or 1
next_state_dist = self.init_dist.pi_0
ret = []
for i in range(word_size):
next_state = sample_discrete(next_state_dist)
ret.append(next_state)
next_state_dist = self.letter_trans.A[next_state]
return tuple(ret)
9.56754688e-04, 9.56754688e-04, 9.56754688e-04, 9.56754688e-04,
9.56754688e-04, 9.56754688e-04, 9.56754688e-04, 9.56754688e-04,
9.56754688e-04, 9.56754688e-04, 9.56754688e-04, 9.56754688e-04,
9.56754688e-04, 9.56754688e-04, 9.56754688e-04, 9.56754688e-04,
9.56754688e-04, 9.56754688e-04, 9.56754688e-04, 9.56754688e-04,
9.56754688e-04, 9.56754688e-04, 9.56754688e-04, 9.56754688e-04
]]
# After setting the parameters and implementing a MixtureDistribution in the pybasicbayes package we can start defining our HSMM.
# In[13]:
dur_distns = []
for state in range(len(state_list)):
dur_distns.append(
PoissonDuration(alpha_0=alpha_0s[state], beta_0=beta_0s[state]))
#dur_distns = [PoissonDuration(alpha_0=alpha_0s[state], beta_0=beta_0s[state])
# for state in range(len(state_list))]
dist_obs_map = [0, 0, 0, 1]
distv = [
Gaussian(mu_0=mu_0s, sigma_0=sigma_0s, kappa_0=kappa_0, nu_0=nu_0),
Categorical(weights=weights, K=len(weights), alpha_0=5)
]
# In[14]:
np.unique([1, 1, 3, 4, 2, 1, 3, 5])
# In[3]:
def resample_dur_dists(self):
self.word_dur_dists = [
PoissonDuration(lmbda=np.sum([self.dur_distns[c].lmbda
for c in w])) for w in self.word_list
]
dur_distns = []
gaussians = []
categoricals = []
mixtures = []
alpha_0s = np.array(alpha_0s)
beta_0s = np.array(beta_0s)
mu_0s = np.array(mu_0s)
sigma_0s = np.array(sigma_0s)
weights = np.array(weights)
dist_obs_map = [0, 0, 0, 1]
for state in range(len(state_list)):
dur_distns.append(PoissonDuration(alpha_0=alpha_0s[state], beta_0=beta_0s[state]))
# dur_distns.append(NegativeBinomialDuration(r=r_s[state], p=p_s[state], k_0=k_0s[state], theta_0=theta_0s[state],
# alpha_0=alpha_0s[state],
# beta_0=beta_0s[state]))
gaussians.append(Gaussian(mu_0=mu_0s[state], sigma_0=sigma_0s[state], kappa_0=kappa_0, nu_0=nu_0))
categoricals.append(Categorical(weights=weights[state, :], K=weights.shape[1], alpha_0=alpha_0))
mixtures.append(DistributionMixture(distv=[gaussians[-1], categoricals[-1]], dist_obs_map=dist_obs_map))
distv = [gaussians, categoricals]
tmat = [
[0.000, 0.760, 0.010, 0.010, 0.210, 0.010], # DX
[0.010, 0.000, 0.430, 0.430, 0.120, 0.010], # place tool
[0.010, 0.450, 0.000, 0.250, 0.250, 0.040], # cutting loop
[0.010, 0.530, 0.210, 0.000, 0.200, 0.050], # coag loop
[0.010, 0.450, 0.200, 0.250, 0.000, 0.050], # clear view
D_latent = 2 # latent linear dynamics' dimension
D_input = 1 # latent linear dynamics' dimension
D_obs = 2 # data dimension
N_iter = 200 # number of VBEM iterations
As = [
np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta),
np.cos(theta)]])
for alpha, theta in ((0.95, 0.1), (0.95, -0.1), (1., 0.))
]
truemodel = ARHSMM(
alpha=4.,
init_state_concentration=4.,
obs_distns=[AutoRegression(A=A, sigma=0.05 * np.eye(2)) for A in As],
dur_distns=[PoissonDuration(alpha_0=3 * 50, beta_0=3) for _ in As])
truemodel.prefix = np.array([[0., 3.]])
data, labels = truemodel.generate(T)
data = data[truemodel.nlags:]
plt.figure()
plt.plot(data[:, 0], data[:, 1], 'x-')
#################
# build model #
#################
Cs = [np.eye(D_obs) for _ in range(Kmax)] # Shared emission matrices
sigma_obss = [0.05 * np.eye(D_obs)
for _ in range(Kmax)] # Emission noise covariances