def comparison_1d():
# Define prior
prior_mean, prior_var = 0.3, 0.01
min_x, max_x = -5, 5
res = 10000
prior = GaussianMixture(1, prior_mean, prior_var)
x_space = np.linspace(min_x, max_x, res)
# Define sensor likelihood
sm = speed_model()
measurement = 'Slow'
measurement_i = sm.class_labels.index(measurement)
# Do a VB update
init_mean, init_var = 0, 1
init_alpha, init_xi = 0.5, np.ones(4)
vb = VariationalBayes()
vb_mean, vb_var, _ = vb.vb_update(measurement, sm, prior, init_mean,
init_var, init_alpha, init_xi)
vb_posterior = GaussianMixture(1, vb_mean, vb_var)
nisar_vb_mean = 0.131005297841171
nisar_vb_var = 6.43335516254277e-05
diff_vb_mean = vb_mean - nisar_vb_mean
diff_vb_var = vb_var - nisar_vb_var
logging.info('Nisar\'s VB update had mean difference {} and var difference {}\n'
.format(diff_vb_mean, diff_vb_var))
# Do a VBIS update
vbis_mean, vbis_var, _ = vb.vbis_update(measurement, sm, prior, init_mean,
init_var, init_alpha, init_xi)
vbis_posterior = GaussianMixture(1, vbis_mean, vbis_var)
nisar_vbis_mean = 0.154223416817080
nisar_vbis_var = 0.00346064073274943
diff_vbis_mean = vbis_mean - nisar_vbis_mean
diff_vbis_var = vbis_var - nisar_vbis_var
logging.info('Nisar\'s VBIS update had mean difference {} and var difference {}\n'
.format(diff_vbis_mean, diff_vbis_var))
# Plot results
likelihood_label = 'Likelihood of \'{}\''.format(measurement)
fig = plt.figure()
ax = fig.add_subplot(111)
sm.classes[measurement].plot(ax=ax, fill_between=False, label=likelihood_label, ls='--')
ax.plot(x_space, prior.pdf(x_space), lw=1, label='prior pdf', c='grey', ls='--')
ax.plot(x_space, vb_posterior.pdf(x_space), lw=2, label='VB posterior', c='r')
ax.fill_between(x_space, 0, vb_posterior.pdf(x_space), alpha=0.2, facecolor='r')
ax.plot(x_space, vbis_posterior.pdf(x_space), lw=2, label='VBIS Posterior', c='g')
ax.fill_between(x_space, 0, vbis_posterior.pdf(x_space), alpha=0.2, facecolor='g')
ax.set_title('VBIS Update')
ax.legend()
ax.set_xlim([0, 0.4])
ax.set_ylim([0, 7])
plt.show()
def vbis_update(self, measurement, likelihood, prior,
init_mean=0, init_var=1, init_alpha=0.5, init_xi=1,
num_samples=None, use_LWIS=False):
"""VB update with importance sampling for Gaussian and Softmax.
"""
if num_samples is None:
num_samples = self.num_importance_samples
if use_LWIS:
q_mu = np.asarray(prior.means[0])
log_c_hat = np.nan
else:
# Use VB update
q_mu, var_VB, log_c_hat = self.vb_update(measurement, likelihood,
prior,
init_mean, init_var,
init_alpha, init_xi)
q_var = np.asarray(prior.covariances[0])
# Importance distribution
q = GaussianMixture(1, q_mu, q_var)
# Importance sampling correction
w = np.zeros(num_samples) # Importance weights
x = q.rvs(size=num_samples) # Sampled points
x = np.asarray(x)
if hasattr(likelihood, 'subclasses'):
measurement_class = likelihood.subclasses[measurement]
else:
measurement_class = likelihood.classes[measurement]
# Compute parameters using samples
w = prior.pdf(x) * measurement_class.probability(state=x) / q.pdf(x)
w /= np.sum(w) # Normalize weights
mu_hat = np.sum(x.T * w, axis=-1)
# <>TODO: optimize this
var_hat = np.zeros_like(np.asarray(q_var))
for i in range(num_samples):
x_i = np.asarray(x[i])
var_hat = var_hat + w[i] * np.outer(x_i, x_i)
var_hat -= np.outer(mu_hat, mu_hat)
# Ensure properly formatted output
if mu_hat.size == 1 and mu_hat.ndim > 0:
mu_post_vbis = mu_hat[0]
else:
mu_post_vbis = mu_hat
if var_hat.size == 1:
var_post_vbis = var_hat[0][0]
else:
var_post_vbis = var_hat
logging.debug('VBIS update found mean of {} and variance of {}.'
.format(mu_post_vbis, var_post_vbis))
return mu_post_vbis, var_post_vbis, log_c_hat
def lwis_update(self, prior):
"""
clustering:
pairwise greedy merging - compare means, weights & variances
salmond's method and runnals' method (better)
"""
prior_mean = np.asarray(prior.means[0])
prior_var = np.asarray(prior.covariances[0])
# Importance distribution
q = GaussianMixture(1, prior_mean, prior_var)
# Importance sampling correction
w = np.zeros(num_samples) # Importance weights
x = q.rvs(size=num_samples) # Sampled points
x = np.asarray(x)
if hasattr(likelihood, 'subclasses'):
measurement_class = likelihood.subclasses[measurement]
else:
measurement_class = likelihood.classes[measurement]
for i in range(num_samples):
w[i] = prior.pdf(x[i]) \
* measurement_class.probability(state=x[i])\
/ q.pdf(x[i])
w /= np.sum(w) # Normalize weights
mu_hat = np.zeros_like(np.asarray(mu_VB))
for i in range(num_samples):
x_i = np.asarray(x[i])
mu_hat = mu_hat + x_i .dot (w[i])
var_hat = np.zeros_like(np.asarray(var_VB))
for i in range(num_samples):
x_i = np.asarray(x[i])
var_hat = var_hat + w[i] * np.outer(x_i, x_i)
var_hat -= np.outer(mu_hat, mu_hat)
if mu_hat.size == 1 and mu_hat.ndim > 0:
mu_lwis = mu_hat[0]
else:
mu_lwis = mu_hat
if var_hat.size == 1:
var_lwis = var_hat[0][0]
else:
var_lwis = var_hat
logging.debug('LWIS update found mean of {} and variance of {}.'
.format(mu_lwis, var_lwis))
return mu_lwis, var_lwis, log_c_hat
class camera_tester(object):
"""docstring for merged_gm"""
def __init__(self, prior, detection_model, trajectory, num_std=1, bounds=None):
self.fig = plt.figure(figsize=(16,8))
self.gm = prior
self.detection_model = detection_model
self.trajectory = itertools.cycle(trajectory)
self.vb = VariationalBayes()
self.num_std = num_std
if bounds is None:
self.bounds = [-5, -5, 5, 5]
else:
self.bounds = bounds
def update(self,i=0):
self.camera_pose = next(self.trajectory)
logging.info('Moving to pose {}.'.format(self.camera_pose))
self.detection_model.move(self.camera_pose)
# Do a VBIS update
mu, sigma, beta = self.vb.update(measurement='No Detection',
likelihood=detection_model,
prior=self.gm,
use_LWIS=True,
poly=detection_model.poly,
num_std=self.num_std
)
self.gm = GaussianMixture(weights=beta, means=mu, covariances=sigma)
# Log what's going on
logging.info(self.gm)
logging.info('Weight sum: {}'.format(beta.sum()))
self.remove()
self.plot()
def plot(self):
levels_res = 50
self.levels = np.linspace(0, np.max(self.gm.pdf(self.pos)), levels_res)
self.contourf = self.ax.contourf(self.xx, self.yy,
self.gm.pdf(self.pos),
levels=self.levels,
cmap=plt.get_cmap('jet')
)
# Plot camera
self.cam_patch = PolygonPatch(self.detection_model.poly, facecolor='none',
linewidth=2, edgecolor='white')
self.ax.add_patch(self.cam_patch)
# Plot ellipses
self.ellipse_patches = self.gm.plot_ellipses(poly=self.detection_model.poly)
def plot_setup(self):
# Define gridded space for graphing
min_x, max_x = self.bounds[0], self.bounds[2]
min_y, max_y = self.bounds[1], self.bounds[3]
res = 30
self.xx, self.yy = np.mgrid[min_x:max_x:1/res,
min_y:max_y:1/res]
pos = np.empty(self.xx.shape + (2,))
pos[:, :, 0] = self.xx; pos[:, :, 1] = self.yy;
self.pos = pos
# Plot setup
self.ax = self.fig.add_subplot(111)
self.ax.set_title('VBIS with camera detection test')
plt.axis('scaled')
self.ax.set_xlim([min_x, max_x])
self.ax.set_ylim([min_y, max_y])
levels_res = 50
self.levels = np.linspace(0, np.max(self.gm.pdf(self.pos)), levels_res)
cax = self.contourf = self.ax.contourf(self.xx, self.yy,
self.gm.pdf(self.pos),
levels=self.levels,
cmap=plt.get_cmap('jet')
)
self.fig.colorbar(cax)
def remove(self):
if hasattr(self, 'cam_patch'):
self.cam_patch.remove()
del self.cam_patch
if hasattr(self, 'ellipse_patches'):
for patch in self.ellipse_patches:
patch.remove()
del self.ellipse_patches
if hasattr(self,'contourf'):
for collection in self.contourf.collections:
collection.remove()
del self.contourf
def gmm_sm_test(measurement='Outside'):
# Define prior
# prior = GaussianMixture(weights=[1, 4, 5],
# means=[[0.5, 1.3], # GM1 mean
# [-0.7, -0.6], # GM2 mean
# [0.2, -3], # GM3 mean
# ],
# covariances=[[[0.4, 0.3], # GM1 mean
# [0.3, 0.4]
# ],
# [[0.3, 0.1], # GM2 mean
# [0.1, 0.3]
# ],
# [[0.5, 0.4], # GM3 mean
# [0.4, 0.5]],
# ])
prior = GaussianMixture(weights=[1, 1, 1, 1, 1],
means=[[-2, -4], # GM1 mean
[-1, -2], # GM2 mean
[0, 0], # GM3 mean
[1, -2], # GM4 mean
[2, -4], # GM5 mean
],
covariances=[[[0.1, 0], # GM1 mean
[0, 0.1]
],
[[0.2, 0], # GM2 mean
[0, 0.2]
],
[[0.3, 0], # GM3 mean
[0, 0.3]
],
[[0.2, 0], # GM4 mean
[0, 0.2]
],
[[0.1, 0], # GM5 mean
[0, 0.1]],
])
# prior = GaussianMixture(weights=[1],
# means=[[-2, -4], # GM1 mean
# ],
# covariances=[[[0.1, 0], # GM1 mean
# [0, 0.1]
# ],
# ])
# Define sensor likelihood
brm = range_model()
# Do a VBIS update
logging.info('Starting VB update...')
vb = VariationalBayes()
mu_hat, var_hat, beta_hat = vb.update(measurement, brm, prior, use_LWIS=True)
vbis_posterior = GaussianMixture(weights=beta_hat, means=mu_hat, covariances=var_hat)
# Define gridded space for graphing
min_x, max_x = -5, 5
min_y, max_y = -5, 5
res = 100
x_space, y_space = np.mgrid[min_x:max_x:1/res,
min_y:max_y:1/res]
pos = np.empty(x_space.shape + (2,))
pos[:, :, 0] = x_space; pos[:, :, 1] = y_space;
levels_res = 50
max_prior = np.max(prior.pdf(pos))
prior_levels = np.linspace(0, max_prior, levels_res)
brm.probability()
max_lh = np.max(brm.probs)
lh_levels = np.linspace(0, max_lh, levels_res)
max_post = np.max(vbis_posterior.pdf(pos))
post_levels = np.linspace(0, max_post, levels_res)
# Plot results
fig = plt.figure()
likelihood_label = 'Likelihood of \'{}\''.format(measurement)
prior_ax = plt.subplot2grid((2,32), (0,0), colspan=14)
prior_cax = plt.subplot2grid((2,32), (0,14), colspan=1)
prior_c = prior_ax.contourf(x_space, y_space, prior.pdf(pos), levels=prior_levels)
cbar = plt.colorbar(prior_c, cax=prior_cax)
prior_ax.set_xlabel('x1')
prior_ax.set_ylabel('x2')
prior_ax.set_title('Prior Distribution')
lh_ax = plt.subplot2grid((2,32), (0,17), colspan=14)
lh_cax = plt.subplot2grid((2,32), (0,31), colspan=1)
brm.classes[measurement].plot(ax=lh_ax, label=likelihood_label, ls='--', levels=lh_levels, show_plot=False, plot_3D=False)
# plt.colorbar(sm.probs, cax=lh_cax)
lh_ax.set_title(likelihood_label)
posterior_ax = plt.subplot2grid((2,32), (1,0), colspan=31)
posterior_cax = plt.subplot2grid((2,32), (1,31), colspan=1)
posterior_c = posterior_ax.contourf(x_space, y_space, vbis_posterior.pdf(pos), levels=post_levels)
plt.colorbar(posterior_c, cax=posterior_cax)
posterior_ax.set_xlabel('x1')
posterior_ax.set_ylabel('x2')
posterior_ax.set_title('VBIS Posterior Distribution')
logging.info('Prior Weights: \n {} \n Means: \n {} \n Variances: \n {} \n'.format(prior.weights,prior.means,prior.covariances))
logging.info('Posterior Weights: \n {} \n Means: \n {} \n Variances: \n {} \n'.format(vbis_posterior.weights,vbis_posterior.means,vbis_posterior.covariances))
plt.show()
def comparison_2d():
# Define prior
prior_mean = np.array([2.3, 1.2])
prior_var = np.array([[2, 0.6], [0.6, 2]])
prior = GaussianMixture(1, prior_mean, prior_var)
# Define sensor likelihood
sm = intrinsic_space_model()
measurement = 'Front'
measurement_i = sm.classes[measurement].id
# Do a VB update
init_mean = np.zeros((1,2))
init_var = np.eye(2)
init_alpha = 0.5
init_xi = np.ones(5)
vb = VariationalBayes()
vb_mean, vb_var, _ = vb.vb_update(measurement, sm, prior, init_mean,
init_var, init_alpha, init_xi)
nisar_vb_mean = np.array([1.795546121012238, 2.512627005425541])
nisar_vb_var = np.array([[0.755723395661314, 0.091742424424428],
[0.091742424424428, 0.747611340151417]])
diff_vb_mean = vb_mean - nisar_vb_mean
diff_vb_var = vb_var - nisar_vb_var
logging.info('Nisar\'s VB update had mean difference: \n {}\n and var difference: \n {}\n'
.format(diff_vb_mean, diff_vb_var))
vb_mean, vb_var, _ = vb.vbis_update(measurement, sm, prior, init_mean,
init_var, init_alpha, init_xi)
vb_posterior = GaussianMixture(1, vb_mean, vb_var)
# Define gridded space for graphing
min_x, max_x = -5, 5
min_y, max_y = -5, 5
res = 200
x_space, y_space = np.mgrid[min_x:max_x:1/res,
min_y:max_y:1/res]
pos = np.empty(x_space.shape + (2,))
pos[:, :, 0] = x_space; pos[:, :, 1] = y_space;
levels_res = 30
max_prior = np.max(prior.pdf(pos))
prior_levels = np.linspace(0, max_prior, levels_res)
sm.probability()
max_lh = np.max(sm.probs)
lh_levels = np.linspace(0, max_lh, levels_res)
max_post = np.max(vb_posterior.pdf(pos))
post_levels = np.linspace(0, max_post, levels_res)
# Plot results
fig = plt.figure()
likelihood_label = 'Likelihood of \'{}\''.format(measurement)
prior_ax = plt.subplot2grid((2,32), (0,0), colspan=14)
prior_cax = plt.subplot2grid((2,32), (0,14), colspan=1)
prior_c = prior_ax.contourf(x_space, y_space, prior.pdf(pos), levels=prior_levels)
cbar = plt.colorbar(prior_c, cax=prior_cax)
prior_ax.set_xlabel('x1')
prior_ax.set_ylabel('x2')
prior_ax.set_title('Prior Distribution')
lh_ax = plt.subplot2grid((2,32), (0,17), colspan=14)
lh_cax = plt.subplot2grid((2,32), (0,31), colspan=1)
sm.classes[measurement].plot(ax=lh_ax, label=likelihood_label, plot_3D=False, levels=lh_levels)
# plt.colorbar(sm.probs, cax=lh_cax)
lh_ax.set_title(likelihood_label)
posterior_ax = plt.subplot2grid((2,32), (1,0), colspan=31)
posterior_cax = plt.subplot2grid((2,32), (1,31), colspan=1)
posterior_c = posterior_ax.contourf(x_space, y_space, vb_posterior.pdf(pos), levels=post_levels)
plt.colorbar(posterior_c, cax=posterior_cax)
posterior_ax.set_xlabel('x1')
posterior_ax.set_ylabel('x2')
posterior_ax.set_title('VB Posterior Distribution')
plt.show()