# calculate posterior predictive distribution via filtering and smoothing at train & test locations:
print('calculating the posterior predictive distribution ...')
t0 = time.time()
posterior_mean, posterior_var, _ = sde_gp_model.predict()
t1 = time.time()
print('prediction time: %2.2f secs' % (t1 - t0))
lb = posterior_mean[:, 0] - 1.96 * posterior_var[:, 0]**0.5
ub = posterior_mean[:, 0] + 1.96 * posterior_var[:, 0]**0.5
x_pred = sde_gp_model.t_all
test_id = sde_gp_model.test_id
print('sampling from the posterior ...')
t0 = time.time()
posterior_samp = sde_gp_model.posterior_sample(20)
t1 = time.time()
print('sampling time: %2.2f secs' % (t1 - t0))
print('plotting ...')
plt.figure(1, figsize=(12, 5))
plt.clf()
plt.plot(x, ground_truth[:, 0, 0], 'k--', label='ground truth')
plt.plot(x, y, 'k.', label='observations')
plt.plot(x_pred, posterior_mean, 'b', label='posterior mean')
plt.fill_between(x_pred, lb, ub, color='b', alpha=0.05, label='95% confidence')
plt.plot(sde_gp_model.t_test, posterior_samp[test_id, 0, :], 'b', alpha=0.15)
plt.xlim([sde_gp_model.t_test[0], sde_gp_model.t_test[-1]])
plt.legend()
plt.title('GP regression via Kalman smoothing')
plt.xlabel('time - $t$')
# calculate posterior predictive distribution via filtering and smoothing at train & test locations:
print('calculating the posterior predictive distribution ...')
t0 = time.time()
nlpd = model.negative_log_predictive_density(t=x_test, y=y_test)
posterior_mean, posterior_cov = model.predict(t=x_plot)
t1 = time.time()
print('prediction time: %2.2f secs' % (t1-t0))
print('test NLPD: %1.2f' % nlpd)
lb = posterior_mean - 1.96 * posterior_cov ** 0.5
ub = posterior_mean + 1.96 * posterior_cov ** 0.5
link_fn = model.likelihood.link_fn
print('sampling from the posterior ...')
t0 = time.time()
posterior_samp = model.posterior_sample(20, t=x_plot)
t1 = time.time()
print('sampling time: %2.2f secs' % (t1-t0))
print('plotting ...')
plt.figure(1, figsize=(12, 5))
plt.clf()
plt.plot(x, y, 'b+', label='training observations')
plt.plot(x_test, y_test, 'r+', alpha=0.4, label='test observations')
plt.plot(x_plot, link_fn(posterior_mean), 'm', label='posterior mean')
plt.fill_between(x_plot, link_fn(lb), link_fn(ub), color='m', alpha=0.05, label='95% confidence')
plt.plot(x_plot, link_fn(posterior_samp), 'm', alpha=0.15)
plt.xlim(x_plot[0], x_plot[-1])
plt.legend()
plt.title('GP classification via Kalman smoothing. Test NLPD: %1.2f' % nlpd)
plt.xlabel('time - $t$')
print('calculating the posterior predictive distribution ...')
t0 = time.time()
posterior_mean, posterior_cov, _, nlpd = model.predict()
t1 = time.time()
print('prediction time: %2.2f secs' % (t1 - t0))
print('test NLPD: %1.2f' % nlpd)
lb = posterior_mean[:, 0, 0] - 1.96 * posterior_cov[:, 0, 0]**0.5
ub = posterior_mean[:, 0, 0] + 1.96 * posterior_cov[:, 0, 0]**0.5
x_pred = model.t_all[:, 0]
test_id = model.test_id
t_test = model.t_all[test_id]
print('sampling from the posterior ...')
t0 = time.time()
posterior_samp = model.posterior_sample(20)
t1 = time.time()
print('sampling time: %2.2f secs' % (t1 - t0))
print('plotting ...')
plt.figure(1, figsize=(12, 5))
plt.clf()
plt.plot(x, y, 'k.', label='training observations')
plt.plot(x_test, y_test, 'r.', alpha=0.4, label='test observations')
plt.plot(x_pred, posterior_mean[..., 0], 'b', label='posterior mean')
plt.fill_between(x_pred, lb, ub, color='b', alpha=0.05, label='95% confidence')
plt.plot(t_test, posterior_samp[test_id, 0, :], 'b', alpha=0.15)
plt.xlim([t_test[0], t_test[-1]])
plt.legend()
plt.title('GP regression via Kalman smoothing. Test NLPD: %1.2f' % nlpd)
plt.xlabel('time - $t$')
