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()
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