def short_state_trace():
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_long)
probs, alphas, betas = fbhmm.forward_backward()
probs_eln, logalphas, logbetas = fbhmm.forward_backward_eln()
state_trace = fbhmm.max_likelihood_state_estimate(probs)
eln_state_trace = fbhmm.max_likelihood_state_estimate(probs_eln)
K = [i for i in range(0, len(y_obs_long) + 1)]
plt.plot(K,
state_trace,
marker='+',
markersize='12',
linestyle='-.',
color='b',
linewidth=2,
drawstyle='steps-mid',
label='Regular FB')
plt.plot(K,
eln_state_trace,
marker='x',
markersize='12',
linestyle=':',
color='r',
linewidth=2,
drawstyle='steps-mid',
label='ELN FB')
yint = range(1, 5)
plt.yticks(yint)
plt.legend(handlelength=4, loc='upper right')
plt.title("State transition chart for Long Dataset")
plt.ylabel("State")
plt.xlabel("Xk")
plt.show()
def posterior_chart():
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_short)
probs, alphas, betas = fbhmm.forward_backward()
print(
tabulate(probs,
headers=[
"K1", "K2", "K3", "K4", "K5", "K6", "K7", "K8", "K9",
"K11", "K11", "K12", "K13", "K14", "K15"
],
tablefmt="latex"))
def posterior_chart():
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_long)
probs, alphas, betas = fbhmm.forward_backward()
probs = np.concatenate((probs.transpose()[:5], probs.transpose()[-5:]),
axis=0).transpose()
print(
tabulate(probs,
headers=[
"X1", "X2", "X3", "X4", "X5", "X42", "X43", "X44", "X45",
"X46"
],
tablefmt="latex"))
def _e_step(self):
"""
For each observation sequence, we store the elngamma and elnxi values. Thus we are running forward-backward with the current
set of parameters for every sequence and storing the resulting log probabilities and log state-state+1 probabilities for each.
These elngamma's and elnxi's are then passed to the maximization step.
"""
elnxis = []
xis = []
elngammas = []
gammas = []
for idx, obs_seq in enumerate(self.sequences):
elngamma, gamma, elnalpha, elnbeta = ForwardBackwardHMM(
self.init, self.trans, self.emis,
obs_seq).forward_backward_eln()
elngammas.append(elngamma[:, 1:])
gammas.append(gamma[:, 1:])
elnxi, xi = self._eln_xi(elnalpha[:, 1:], elnbeta[:, 1:], obs_seq)
elnxis.append(elnxi)
xis.append(xi)
return elnxis, xis, elngammas, gammas
def state_trace():
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_short)
probs_eln, logalphas, logbetas = fbhmm.forward_backward_eln()
exact_state_trace = fbhmm.max_likelihood_state_estimate(probs_eln)
vhmm = ViterbiHMM(pxk_xkm1, pyk_xk, px0, y_obs_short)
path, log_probs = vhmm.viterbi_path()
K = [i for i in range(0, len(y_obs_short) + 1)]
plt.plot(K,
exact_state_trace,
marker='+',
markersize='12',
linestyle='-.',
color='b',
linewidth=2,
drawstyle='steps-mid',
label='Exact Inference')
plt.plot(K,
path,
marker='x',
markersize='12',
linestyle=':',
color='r',
linewidth=2,
drawstyle='steps-mid',
label='Viterbi')
yint = range(1, 5)
plt.yticks(yint)
plt.legend(handlelength=6)
plt.title(
"State Transition Comparing Exact vs. Viterbi MAP Inference | Short HMM"
)
plt.ylabel("State")
plt.xlabel("Xk")
plt.show()
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_long)
probs_eln, logalphas, logbetas = fbhmm.forward_backward_eln()
exact_state_trace = fbhmm.max_likelihood_state_estimate(probs_eln)
vhmm = ViterbiHMM(pxk_xkm1, pyk_xk, px0, y_obs_long)
path, log_probs = vhmm.viterbi_path()
K = [i for i in range(0, len(y_obs_long) + 1)]
plt.plot(K,
exact_state_trace,
marker='+',
markersize='12',
linestyle='-.',
color='b',
linewidth=2,
drawstyle='steps-mid',
label='Exact Inference')
plt.plot(K,
path,
marker='x',
markersize='12',
linestyle=':',
color='r',
linewidth=2,
drawstyle='steps-mid',
label='Viterbi')
yint = range(1, 5)
plt.yticks(yint)
plt.legend(handlelength=6)
plt.title(
"State Transition Comparing Exact vs. Viterbi MAP Inference | Long HMM"
)
plt.ylabel("State")
plt.xlabel("Xk")
plt.show()
def data_likelihood():
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_long)
probs, alphas, betas = fbhmm.forward_backward()
print(eln(sum(alphas[:, len(y_obs_long)])))
def state_trace():
lli = LikelihoodSamplingInference(pxk_xkm1, pyk_xk, px0, y_obs_short)
print("Running approximate inference with 100 samples...")
state_trace_100 = lli.max_likelihood_state_estimate(lli.run_inference(100))
print("Running approximate inference with 1000 samples...")
state_trace_1000 = lli.max_likelihood_state_estimate(
lli.run_inference(1000))
print("Running approximate inference with 10000 samples...")
state_trace_10000 = lli.max_likelihood_state_estimate(
lli.run_inference(10000))
print("Running exact inference...")
fbhmm = ForwardBackwardHMM(pxk_xkm1, pyk_xk, px0, y_obs_short)
probs_eln, logalphas, logbetas = fbhmm.forward_backward_eln()
exact_state_trace = fbhmm.max_likelihood_state_estimate(probs_eln)
K = [i for i in range(0, len(y_obs_short) + 1)]
print(
"Plotting 'State Transition Comparing Exact vs. 100 Sample Approximate Inference'..."
)
plt.plot(K,
exact_state_trace,
marker='+',
markersize='12',
linestyle='-.',
color='b',
linewidth=2,
drawstyle='steps-mid',
label='Exact Inference')
plt.plot(K,
state_trace_100,
marker='x',
markersize='12',
linestyle=':',
color='r',
linewidth=2,
drawstyle='steps-mid',
label='LW - 100 Samples')
yint = range(1, 5)
plt.yticks(yint)
plt.legend(handlelength=6)
plt.title(
"State Transition Comparing Exact vs. 100 Sample Approximate Inference"
)
plt.ylabel("State")
plt.xlabel("Xk")
plt.show()
print(
"Plotting 'State Transition Comparing Exact vs. 1000 Sample Approximate Inference'..."
)
plt.plot(K,
exact_state_trace,
marker='+',
markersize='12',
linestyle='-.',
color='b',
linewidth=2,
drawstyle='steps-mid',
label='Exact Inference')
plt.plot(K,
state_trace_1000,
marker='x',
markersize='12',
linestyle=':',
color='r',
linewidth=2,
drawstyle='steps-mid',
label='LW - 1000 Samples')
yint = range(1, 5)
plt.yticks(yint)
plt.legend(handlelength=6)
plt.title(
"State Transition Comparing Exact vs. 1000 Sample Approximate Inference"
)
plt.ylabel("State")
plt.xlabel("Xk")
plt.show()
print(
"Plotting 'State Transition Comparing Exact vs. 10000 Sample Approximate Inference'..."
)
plt.plot(K,
exact_state_trace,
marker='+',
markersize='12',
linestyle='-.',
color='b',
linewidth=2,
drawstyle='steps-mid',
label='Exact Inference')
plt.plot(K,
state_trace_10000,
marker='x',
markersize='12',
linestyle=':',
color='r',
linewidth=2,
drawstyle='steps-mid',
label='LW - 10000 Samples')
yint = range(1, 5)
plt.yticks(yint)
plt.legend(handlelength=6)
plt.title(
"State Transition Comparing Exact vs. 10000 Sample Approximate Inference"
)
plt.ylabel("State")
plt.xlabel("Xk")
plt.show()
def _e_step(self, obs_seq):
return ForwardBackwardHMM(self.init, self.trans, self.emis,
obs_seq).forward_backward_eln()