# Set bounding box used by DEFT
bbox = [-5.0, 10.0]
# Perform density estimation using DEFT
start_time = time.clock()
#
# DO THIS If all you want is the distribution function
#
#Q_star = deft_1d(xs, G=G, alpha=alpha, bbox=bbox)
#
# DO THIS If all you want details of the computation
#
Q_star, results = deft_1d(xs, G=G, alpha=alpha, bbox=bbox, details=True)
s = 'deft_1d with G=%d and alpha=%d took %.2f sec' % (G, alpha, time.clock() -
start_time)
###
### Plot results
###
# Close existing figure and create new figure
plt.close('all')
plt.figure()
# Plot histogram
plt.hist(xs,
G,
G = 100
# Specify N and alphas
N = 100
alpha = 2
num_samples = 20
# Draw data, rescaled to give an xint of length L = 10, centered on 0
xint = sp.array([-5.0, 5.0])
[xis, xint, Q_true, Q_true_details] = draw_from_gaussian_mix(N=N, Nx=G, gaussians=gaussians, xint=xint)
xmid = sp.mean(xint)
xspan = xint - xmid
gaussians = Q_true_details.gaussians
# Perform DEFT density estimation
Q_star, Q_star_details = deft_1d(xis, xmid+xspan, alpha=alpha, G=G, details=True, num_samples=20, tf_shift=-3, verbose=True)
Q_star_wide3, Q_star_wide3_details = deft_1d(xis, xmid+3*xspan, alpha=alpha, G=3*G, details=True, verbose=True)
Q_star_wide10, Q_star_wide10_details = deft_1d(xis, xmid+10*xint, alpha=alpha, G=10*G, details=True, verbose=True)
Q_star_fine, Q_star_fine_details = deft_1d(xis, xmid+xspan, alpha=alpha, G=3*G, details=True, verbose=True)
Q_star_coarse, Q_star_coarse_details = deft_1d(xis, xmid+xspan, alpha=alpha, G=int(G/3), details=True, verbose=True)
Q_star_alpha1, Q_star_alpha1_details = deft_1d(xis, xmid+xspan, alpha=1, G=G, details=True, verbose=True)
Q_star_alpha3, Q_star_alpha3_details = deft_1d(xis, xmid+xspan, alpha=3, G=G, details=True, verbose=True)
# Design plotting grid
xs = sp.linspace(xint[0], xint[1], 10000)
# Save everything
things = {}
things['Q_star_details'] = Q_star_details
things['Q_true_details'] = Q_true_details
things['Q_star_wide3_details'] = Q_star_wide3_details
# Set bounding box used by DEFT
bbox = [-5.0, 10.0]
# Perform density estimation using DEFT
start_time = time.clock()
#
# DO THIS If all you want is the distribution function
#
# Q_star = deft_1d(xs, G=G, alpha=alpha, bbox=bbox)
#
# DO THIS If all you want details of the computation
#
Q_star, results = deft_1d(xs, G=G, alpha=alpha, bbox=bbox, details=True)
s = "deft_1d with G=%d and alpha=%d took %.2f sec" % (G, alpha, time.clock() - start_time)
###
### Plot results
###
# Close existing figure and create new figure
plt.close("all")
plt.figure()
# Plot histogram
plt.hist(xs, G, normed=1, histtype="stepfilled", edgecolor="none", facecolor="gray")
# Plot estimated density and true density
def get_pdfs_from_data(data, method="deft", G=200, alpha=3, bbox="adjust", factor=0.5,
verbose=False):
""" Performs a non-parametric estimation of the densities in data and returns
a list compatible with the npfi function defined above.
If DEFT is used for the estimates, it uses the same bounding box for all
PDFs. This bounding box should be used when calling npfi.
Args:
data: A list of arrays containing the sample data.
method: Either "deft" or "gaussian_kde" for the non-parametric
estimation method.
G: parameter to be passed to DEFT if used [2].
alpha: parameter to be passed to DEFT if used [2].
bbox: Either "adjust" or a bounding box (tuple with two values). Used
for DEFT only.
factor: If bbox is "adjust", by which factor to adjust.
verbose: If set to true, print out debug info such as run times.
Returns:
pdfs: a list of the estimated pdfs
bbox: the appropriate bounding box
"""
assert hasattr(data, '__iter__')
assert isinstance(method, str) and method in ["deft", "gaussian_kde"]
if method == "deft" and not HAS_DEFT:
raise Exception("DEFT has been disabled.")
assert isinstance(G, (int, long))
assert isinstance(alpha, (int, long)) and alpha > 0
assert isinstance(factor, (int, long, float)) and factor > 0
assert (isinstance(bbox, str) and bbox == "adjust") or \
(len(bbox) == 2 and bbox[0] < bbox[1])
# Track time
if verbose:
start = timeit.default_timer()
# Get the bounding box if necessary
if method is "deft" and bbox is "adjust":
bbox = get_bbox(data, multi_dim=True, factor=factor)
if method is "gaussian_kde":
bbox = (-np.inf, np.inf)
# Estimate the PDFs
pdfs = []
for d in data:
if method is "gaussian_kde":
pdfs.append(gaussian_kde(d))
else:
pdfs.append(deft_1d(d, G=G, alpha=alpha, bbox=bbox))
if verbose:
print("PDF estimation took %.2f with %s" % (timeit.default_timer()-start, method))
return pdfs, bbox
# Draw data from mixture
[xis, xgrid, Q_true, other] = draw_from_gaussian_mix(N=N, Nx=G, gaussians=gaussians)
# Compute data range and grid for fine-graned analysis
xmin = min(xgrid)
xmax = max(xgrid)
xint = [xmin, xmax]
xs = sp.linspace(xmin, xmax, plot_grid_size)
dx = xs[1]-xs[0]
# Interpolate Q_true for plotting
Q_true_vals = Q_true(xs)
# Perform DEFT density estimation
Q_star1_vals = deft_1d(xis, xint, alpha=1, G=G, verbose=False)(xs)
Q_star2_vals = deft_1d(xis, xint, alpha=2, G=G, verbose=False)(xs)
Q_star3_vals = deft_1d(xis, xint, alpha=3, G=G, verbose=False)(xs)
# Perform GKDE denstiy estimation
gkde = gaussian_kde(xis)
Q_gkde_vals = gkde(xs)/sum(gkde(xs)*dx)
# Perform GMM denstiy estimation using BIC
max_K = 10
bic_values = sp.zeros([max_K]);
Qs_gmm = sp.zeros([max_K,plot_grid_size])
for k in sp.arange(1,max_K+1):
gmm = mixture.GMM(int(k))
gmm.fit(xis)
Qgmm = lambda(x): sp.exp(gmm.score(x))/sum(sp.exp(gmm.score(xs))*dx)
# Draw data from mixture
[xis, xgrid, Q_true,
other] = draw_from_gaussian_mix(N=N, Nx=G, gaussians=gaussians)
# Compute data range and grid for fine-graned analysis
xmin = min(xgrid)
xmax = max(xgrid)
xint = [xmin, xmax]
xs = sp.linspace(xmin, xmax, plot_grid_size)
dx = xs[1] - xs[0]
# Interpolate Q_true for plotting
Q_true_vals = Q_true(xs)
# Perform DEFT density estimation
Q_star1_vals = deft_1d(xis, xint, alpha=1, G=G, verbose=False)(xs)
Q_star2_vals = deft_1d(xis, xint, alpha=2, G=G, verbose=False)(xs)
Q_star3_vals = deft_1d(xis, xint, alpha=3, G=G, verbose=False)(xs)
# Perform GKDE denstiy estimation
gkde = gaussian_kde(xis)
Q_gkde_vals = gkde(xs) / sum(gkde(xs) * dx)
# Perform GMM denstiy estimation using BIC
max_K = 10
bic_values = sp.zeros([max_K])
Qs_gmm = sp.zeros([max_K, plot_grid_size])
for k in sp.arange(1, max_K + 1):
gmm = mixture.GMM(int(k))
gmm.fit(xis)
Qgmm = lambda (x): sp.exp(gmm.score(x)) / sum(
###
### Perform density estimation using deft_1d
###
# Set number of grid points used by DEFT
G = 100
# Set power of derivative to constrain
alpha = 3
# Set bounding box used by DEFT
bbox = [-5.0, 10.0]
# Perform density estimation using DEFT
start_time = time.clock()
Q_star = deft_1d(xs, G=G, alpha=alpha, bbox=bbox)
s = 'deft_1d with G=%d and alpha=%d took %.2f sec'%(G,alpha,time.clock()-start_time)
###
### Plot results
###
# Close existing figure and create new figure
plt.close('all')
plt.figure()
# Plot histogram
plt.hist(xs, G, normed=1, histtype='stepfilled', edgecolor='none', facecolor='gray')
# Plot estimated density and true density
xgrid = sp.linspace(bbox[0], bbox[1], 1000)