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missing_data.py
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missing_data.py
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from __future__ import division
import numpy as np
import numpy.random as npr
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from pybasicbayes.distributions import Regression, DiagonalRegression, Gaussian
from pybasicbayes.util.text import progprint_xrange
from pyslds.models import HMMSLDS, WeakLimitStickyHDPHMMSLDS
npr.seed(0)
#########################
# set some parameters #
#########################
K, Kmax, D_obs, D_latent = 2, 10, 4, 2
mu_init = np.zeros(D_latent)
mu_init[0] = 1.0
sigma_init = 0.01*np.eye(D_latent)
def random_rotation(n,theta):
rot = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
out = np.zeros((n,n))
out[:2,:2] = rot
q = np.linalg.qr(np.random.randn(n,n))[0]
return q.dot(out).dot(q.T)
As = [0.99 * random_rotation(D_latent, np.pi/24.),
0.99 * random_rotation(D_latent, np.pi/12.)]
C = np.random.randn(D_obs, D_latent)
sigma_obs = 0.5 * np.ones(D_obs)
###################
# generate data #
###################
init_dynamics_distns = [Gaussian(mu=mu_init, sigma=sigma_init) for _ in range(K)]
dynamics_distns = [Regression(A=A, sigma=np.eye(D_latent)) for A in As]
emission_distns = DiagonalRegression(D_obs, D_latent, A=C, sigmasq=sigma_obs)
truemodel = HMMSLDS(
dynamics_distns=dynamics_distns,
emission_distns=emission_distns,
init_dynamics_distns=init_dynamics_distns,
alpha=3., init_state_distn='uniform')
# Manually create the states object with the mask
T = 1000
stateseq = np.repeat(np.arange(T//100) % 2, 100).astype(np.int32)
statesobj = truemodel._states_class(model=truemodel, T=stateseq.size, stateseq=stateseq)
statesobj.generate_gaussian_states()
data = statesobj.data = statesobj.generate_obs()
gaussian_states = statesobj.gaussian_states
truemodel.states_list.append(statesobj)
# Mask off a chunk of data
# mask = npr.rand(*data.shape) < 0.5
mask = np.ones_like(data, dtype=bool)
chunksz = 200
for i,offset in enumerate(range(0,T,chunksz)):
j = i % (D_obs + 1)
if j < D_obs:
mask[offset:min(offset+chunksz, T), j] = False
if j == D_obs:
mask[offset:min(offset+chunksz, T), :] = False
statesobj.mask = mask
###############
# make model #
###############
model = HMMSLDS(
init_dynamics_distns=
[Gaussian(
nu_0=5, sigma_0=3.*np.eye(D_latent),
mu_0=np.zeros(D_latent), kappa_0=0.01,
mu=mu_init, sigma=sigma_init
) for _ in range(Kmax)],
dynamics_distns=
[Regression(
A=np.eye(D_latent), sigma=np.eye(D_latent),
nu_0=D_latent+3,
S_0=D_latent*np.eye(D_latent),
M_0=np.eye(D_latent),
K_0=D_latent*np.eye(D_latent),
) for _ in range(Kmax)],
emission_distns=
DiagonalRegression(
D_obs, D_latent,
alpha_0=2.0, beta_0=1.0,
),
alpha=3., init_state_distn='uniform')
model.add_data(data=data, mask=mask)
###############
# fit model #
###############
N_init_samples = 0
for _ in progprint_xrange(N_init_samples):
model.resample_model()
model._init_mf_from_gibbs()
N_iters = 100
def update(model):
model.VBEM_step()
# model.meanfield_coordinate_descent_step()
lp = model.log_likelihood()
smoothed_obs = model.states_list[0].smooth()
return lp, model.stateseqs[0], smoothed_obs
# Fit the model
lls, z_smpls, smoothed_obss = zip(*[update(model) for _ in progprint_xrange(N_iters)])
################
# likelihoods #
################
plt.figure(figsize=(10,6))
plt.plot(lls[1:],'-b')
plt.plot([0, N_iters - 1], truemodel.log_likelihood() * np.ones(2), '-k')
plt.xlabel('iteration')
plt.ylabel('log likelihood')
################
# smoothing #
################
plt.figure(figsize=(10,6))
given_data = data.copy()
given_data[~mask] = np.nan
masked_data = data.copy()
masked_data[mask] = np.nan
ylims = (-1.1*abs(data).max(), 1.1*abs(data).max())
xlims = (0, min(T,1000))
N_subplots = min(D_obs,4)
for i in range(N_subplots):
plt.subplot(N_subplots,1,i+1,aspect="auto")
plt.plot(given_data[:,i], 'k', label="observed")
plt.plot(masked_data[:,i], ':k', label="masked")
plt.plot(smoothed_obss[-1][:,i], 'b', lw=2, label="smoothed")
plt.imshow(1-mask[:,i][None,:],cmap="Greys",alpha=0.25,extent=(0,T) + ylims, aspect="auto")
if i == 0:
plt.legend(loc="upper center", ncol=3, bbox_to_anchor=(0.5, 1.5))
if i == N_subplots - 1:
plt.xlabel('time index')
plt.ylabel("$x_%d(t)$" % (i+1))
plt.ylim(ylims)
plt.xlim(xlims)
# plt.savefig("slds_missing_data_ex.png")
################
# z samples #
################
fig = plt.figure(figsize=(8,4))
gs = gridspec.GridSpec(6,1)
ax1 = fig.add_subplot(gs[:-1])
ax2 = fig.add_subplot(gs[-1])
im = ax1.imshow(np.array(z_smpls), aspect='auto', interpolation="none")
ax1.autoscale(False)
ax1.set_ylabel("Iteration")
ax1.set_xticks([])
ax2.imshow(truemodel.stateseqs[0][None,:], aspect='auto')
ax2.set_ylabel("True", labelpad=27)
ax2.set_xlabel("Time")
ax2.set_yticks([])
fig.suptitle("Discrete state samples")
# plt.savefig("slds_discrete_states.png")
plt.show()