pdf, xs, kde_best = kde_1d.kde(data,G,bbox,details=True) sigma = kde_best.bandwidth plt.figure() xs_fine = sp.linspace(bbox[0],bbox[1],1E4) kernels = sp.zeros([len(xs_fine),num_samples]) for i, datum in enumerate(data): kernels[:,i] = gaussian(x=xs_fine,mu=datum,sigma=sigma) plt.plot(xs_fine,kernels,'-b',alpha=0.2) plt.plot(xs,pdf,'-b',linewidth=2) plt.show() # Do density estimation results = deft_1d.run(data, G=G, alpha=alpha, bbox=bbox) xs_hist = results.bin_edges[:-1] xs = results.bin_centers bin_centers = results.bin_centers R = results.R Q_star = results.Q_star h = results.h i_star = results.map_curve.i_star # Plot histogram with density estimate on top plt.figure(figsize=[3, 8]) # Set Qs along MAP curve to plot Qs = [[], results.map_curve.points[0].Q, results.map_curve.points[i_star - 20].Q,
orange = [1., 0.5, 0.]
gray = [0.6, 0.6, 0.6]
# Simulate data and get default deft settings
data, defaults = simulate_data_1d.run(data_type, N)
# Get bounding box
bbox = [defaults['box_min'], defaults['box_max']]
#
# Do DEFT density estimation
#
results = deft_1d.run(data, G=G, alpha=alpha, \
bbox=bbox, \
periodic=False,
num_samples=100,
print_t=True)
# Provide feedback
print '\n%s, alpha=%d' % (data_type, alpha)
# Compute true density
xs = results.bin_centers
Q_true = np.zeros(G)
for i, x in enumerate(xs):
Q_true[i] = eval(defaults['pdf_py'])
Q_true /= results.h * sum(Q_true)
#
# Estimate entropy
for d, data_type in enumerate(data_types):
# Simulate data and get default deft settings
data, defaults = simulate_data_1d.run(data_type, N)
# Iterate over value sfor alpha
for a, alpha in enumerate(alphas):
# Specify subplot
ax = plt.subplot(num_rows, num_cols, num_cols * d + a + 1)
bbox = [defaults['box_min'], defaults['box_max']]
# Do density estimation
results = deft_1d.run(data, G=G, alpha=alpha, \
bbox=bbox, \
periodic=defaults['periodic'])
# Plot histogram density
left_bin_edges = results.bin_edges[:-1]
plt.bar(left_bin_edges, results.R, \
width=results.h, linewidth=0, color=gray, zorder=0)
# Plot error bars on density estimate
plt.fill_between(results.bin_centers,
results.Q_ub,
results.Q_lb,
color=lightblue,
zorder=1,
alpha=0.5,
linewidth=0)
mis[i] = mutual_information(Q_xy)
# Compute mean and variance of the differential entropy
mi_mean = np.mean(mis)
mi_std = np.std(mis)
results.mi_compute_time = time.clock() - entropy_start_time
# Estimate distribution of mutual information estimates
# Now do density estimation for the entropies
mi_G = 100
mi_box = [max(0., mi_mean - 5 * mi_std), mi_mean + 5 * mi_std]
mi_box[0] = min(mi_box[0], mi_true)
mi_box[1] = max(mi_box[1], mi_true)
mi_results = deft_1d.run(mis,
G=mi_G,
bbox=mi_box,
alpha=3,
periodic=False,
num_samples=0)
#Q, R, Q_ub, Q_lb, Q_samples, map_curve
Q = results.Q_star
R = results.R
map_curve = results.map_curve
# Make Q 2d
Q_2d = Q.reshape(num_bins)
R_2d = R.reshape(num_bins)
# Calibrate both R and Q to the same scale
cl = [0.0, max(Q_true.ravel())]
cmap = plt.get_cmap('bone')
orange = [1., 0.5, 0.]
gray = [0.6, 0.6, 0.6]
# Generate data
N = 100
G = 100
alpha = 3
data_type = 'gaussian'
# Compute data set
data, defaults = simulate_data_1d.run(data_type, N)
# Do density estimation
results = deft_1d.run(data, G=G, alpha=alpha, \
bbox=defaults.bbox, \
periodic=defaults.periodic)
# Plot the MAP curve
map_curve = results.map_curve
points = map_curve.get_points()
ts = sp.array([p.t for p in points])
num_points = len(points)
Qs = sp.zeros([G, num_points])
for n, p in enumerate(points):
Qs[:, n] = p.Q
log_Es, ts = map_curve.get_log_evidence_ratios(finite=True)
# Simulate data and get default deft settings
data, defaults = simulate_data_1d.run(data_type, N)
# Get bounding box
bbox = [defaults['box_min'], defaults['box_max']]
#
# Do DEFT density estimation
#
results = deft_1d.run(data, G=G, alpha=alpha, \
bbox=bbox, \
periodic=False,
num_samples=100,
errorbars=False,
print_t=False,
ell_guess=ell_guess,
resolution=resolution,
tollerance=tollerance)
# Provide feedback
print '\n%s, alpha=%d' % (data_type, alpha)
print 'laplacian_compute_time == %.2f sec' % results.laplacian_compute_time
print 'map_curve_compute_time == %.2f sec' % results.map_curve_compute_time
#print 'errorbar_compute_time == %.2f sec'%results.errorbar_compute_time
print 'posterior_sample_compute_time == %.2f sec'%results.\
posterior_sample_compute_time
print 'copy_compute_time == %.2f sec' % results.copy_compute_time
print 'entropy_compute_time == %.2f sec' % results.entropy_compute_time
print 'deft_1d_compute_time == %.2f sec' % results.deft_1d_compute_time