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vbem.py
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vbem.py
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from __future__ import division
import numpy as np
import numpy.random as npr
import matplotlib.pyplot as plt
from pyhsmm.basic.distributions import PoissonDuration
from autoregressive.models import ARHSMM
from autoregressive.distributions import AutoRegression
from pyhsmm.util.text import progprint_xrange
from pybasicbayes.distributions import DiagonalRegression, Gaussian, Regression
from pyslds.models import HMMSLDS
np.random.seed(0)
###################
# generate data #
###################
T = 1000
Kmax = 10 # number of latent discrete states
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
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=np.zeros(D_latent), sigma=np.eye(D_latent)
) for _ in range(Kmax)],
dynamics_distns=
[Regression(
A=np.hstack((np.eye(D_latent), np.zeros((D_latent, D_input)))),
sigma=np.eye(D_latent),
nu_0=D_latent+3,
S_0=D_latent*np.eye(D_latent),
M_0=np.hstack((np.eye(D_latent), np.zeros((D_latent, D_input)))),
K_0=D_latent*np.eye(D_latent + D_input),
) for _ in range(Kmax)],
emission_distns=
DiagonalRegression(
D_obs, D_latent + D_input,
alpha_0=2.0, beta_0=1.0,
),
alpha=3., init_state_distn='uniform')
model.add_data(data, inputs=np.ones((T, D_input)))
model.resample_states()
for _ in progprint_xrange(0):
model.resample_model()
model.states_list[0]._init_mf_from_gibbs()
####################
# run mean field #
####################
vlbs = []
for _ in progprint_xrange(N_iter):
model.VBEM_step()
vlbs.append(model.VBEM_ELBO())
if len(vlbs) > 1:
assert vlbs[-1] > vlbs[-2] - 1e-8
plt.figure()
plt.plot(vlbs)
# plt.plot([0, N_iter], truemodel.log_likelihood(data) * np.ones(2), '--k')
plt.xlabel("Iteration")
plt.ylabel("VLB")
import matplotlib.gridspec as gridspec
fig = plt.figure(figsize=(9,3))
gs = gridspec.GridSpec(7,1)
ax1 = fig.add_subplot(gs[:-2])
ax2 = fig.add_subplot(gs[-2], sharex=ax1)
ax3 = fig.add_subplot(gs[-1], sharex=ax1)
im = ax1.matshow(model.states_list[0].expected_states.T, aspect='auto', cmap="Greys")
ax1.set_xticks([])
ax1.set_yticks(np.arange(Kmax))
ax1.set_ylabel("Discrete State")
ax2.imshow(model.states_list[0].expected_states.argmax(1)[None,:],
vmin=0, vmax=Kmax, aspect='auto')
ax2.set_xticks([])
ax2.set_yticks([])
ax3.matshow(labels[None,:], aspect='auto')
ax3.set_xticks([])
ax3.set_yticks([])
ax3.set_xlabel("Time")
plt.show()