def _make_model(self):
data = self.model_data
# The parameters are:
# Gaussian observation distributions (ellipses in red-green intensity space)
# mu_0 and sigma parameterize our prior belief about the means and sigma of each state
# nu_0 expresses your confidence in the prior--it's the number of data points that
# you claim got you these prior parameters. Nu_0 has to be strictly bigger than the
# number of dimensions (2, in our case). You could do 2.01.
# The nominal covariance is sigma_0/nu_0, so hence the 3 in sigma_0.
# kappa_0: Uncertainty in the mean should be related to uncertainty in the covariance.
# kappa_0 is an amplitude for that. Smaller number means other states' means will be
# further away.
obs_hypparams = dict(
mu_0=data.mean(0),
sigma_0=3. * cov(data),
nu_0=3.,
kappa_0=0.5,
)
# In the function call below:
# (1) alpha and gamma bias how many states there are. We're telling it to expect
# one state (conservative)
# (2) kappa controls the self-transition bias. Bigger number means becomes more expensive
# for states to non-self-transition (that is, change to a different state).
model = WeakLimitStickyHDPHMM(
alpha=1.,
gamma=1.,
init_state_distn='uniform',
kappa=500.,
obs_distns=[Gaussian(**obs_hypparams) for _ in range(10)],
)
return model
data, labels = truemodel.generate(T)
plt.figure()
truemodel.plot()
plt.gcf().suptitle('True model')
##################
# set up model #
##################
Nmax = 20
obs_distns = \
[pyhsmm.distributions.Gaussian(
mu_0=data.mean(0),
sigma_0=0.5*cov(data),
kappa_0=0.5,
nu_0=obs_dim+3) for state in range(Nmax)]
dur_distns = \
[pyhsmm.distributions.NegativeBinomialIntegerRVariantDuration(
np.r_[0,0,0,0,0,1.,1.,1.], # discrete distribution uniform over {6,7,8}
alpha_0=9,beta_0=1, # average geometric success probability 1/(9+1)
) for state in range(Nmax)]
model = pyhsmm.models.HSMMIntNegBinVariant(
init_state_concentration=10.,
alpha=6.,gamma=6.,
obs_distns=obs_distns,
dur_distns=dur_distns)
model.add_data(data,left_censoring=True)
def pca(data, num_components=2):
U, s, Vh = np.linalg.svd(cov(data))
return Vh.T[:, :num_components]
data, labels = truemodel.generate(T)
plt.figure()
truemodel.plot()
plt.gcf().suptitle('True model')
##################
# set up model #
##################
Nmax = 20
obs_distns = \
[pyhsmm.distributions.Gaussian(
mu_0=data.mean(0),
sigma_0=0.5*cov(data),
kappa_0=0.5,
nu_0=obs_dim+3) for state in range(Nmax)]
dur_distns = \
[pyhsmm.distributions.NegativeBinomialIntegerRVariantDuration(
np.r_[0,0,0,0,0,1.,1.,1.], # discrete distribution uniform over {6,7,8}
alpha_0=9,beta_0=1, # average geometric success probability 1/(9+1)
) for state in range(Nmax)]
model = pyhsmm.models.HSMMIntNegBinVariant(init_state_concentration=10.,
alpha=6.,
gamma=6.,
obs_distns=obs_distns,
dur_distns=dur_distns)
model.add_data(data, left_censoring=True)
###############
# load data #
###############
data = np.loadtxt("example-data.txt")
T, obs_dim = data.shape
##################
# set up model #
##################
Nmax = 20
obs_distns = [
pyhsmm.distributions.Gaussian(mu_0=data.mean(0), sigma_0=0.5 * cov(data), kappa_0=0.5, nu_0=obs_dim + 3)
for state in range(Nmax)
]
dur_distns = [
pyhsmm.distributions.NegativeBinomialDuration(7 * 100, 1.0 / 100, 50 * 10, 50 * 1) for state in range(Nmax)
]
model = pyhsmm.models.HSMMGeoApproximation(
init_state_concentration=Nmax, # doesn't matter for one chain
alpha=6.0,
gamma=6.0,
obs_distns=obs_distns,
dur_distns=dur_distns,
trunc=150,
) # NOTE: blows up this isn't long enough wrt the NegativeBinomial parameters
def pca(data, num_components=2):
U, s, Vh = np.linalg.svd(cov(data))
return Vh.T[:, :num_components]