def test_1D_density():
np.random.seed(0)
dist = norm(0, 1)
X = dist.rvs((5000, 1))
X2 = np.linspace(-5, 5, 10).reshape((10, 1))
true_dens = dist.pdf(X2[:, 0]) * X.shape[0]
classifiers = [KDE('gaussian', h=0.1),
KDE('tophat', h=0.2),
KDE('exponential', h=0.1),
KDE('quadratic', h=0.2),
KNeighborsDensity(method='simple', n_neighbors=250),
KNeighborsDensity(method='bayesian', n_neighbors=250)]
for clf in classifiers:
yield (check_1D_density, clf, X, X2, true_dens, 100)
#------------------------------------------------------------
# Create the grid on which to evaluate the results
Nx = 50
Ny = 125
xmin, xmax = (-375, -175)
ymin, ymax = (-300, 200)
#------------------------------------------------------------
# Evaluate for several models
Xgrid = np.vstack(
map(np.ravel,
np.meshgrid(np.linspace(xmin, xmax, Nx), np.linspace(ymin, ymax,
Ny)))).T
kde = KDE(metric='gaussian', h=5)
dens_KDE = kde.fit(X).eval(Xgrid).reshape((Ny, Nx))
knn5 = KNeighborsDensity('bayesian', 5)
dens_k5 = knn5.fit(X).eval(Xgrid).reshape((Ny, Nx))
knn40 = KNeighborsDensity('bayesian', 40)
dens_k40 = knn40.fit(X).eval(Xgrid).reshape((Ny, Nx))
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 2.2))
fig.subplots_adjust(left=0.12,
right=0.95,
bottom=0.2,
top=0.9,
N_values = (500, 5000)
subplots = (211, 212)
k_values = (10, 100)
for N, k, subplot in zip(N_values, k_values, subplots):
ax = fig.add_subplot(subplot)
xN = x[:N]
t = np.linspace(-10, 30, 1000)
# Compute density with KDE
if use_sklearn_KDE:
kde = KernelDensity(0.1, kernel='gaussian')
kde.fit(xN[:, None])
dens_kde = np.exp(kde.score_samples(t[:, None]))
else:
kde = KDE('gaussian', h=0.1).fit(xN[:, None])
dens_kde = kde.eval(t[:, None]) / N
# Compute density with Bayesian nearest neighbors
nbrs = KNeighborsDensity('bayesian', n_neighbors=k).fit(xN[:, None])
dens_nbrs = nbrs.eval(t[:, None]) / N
# plot the results
ax.plot(t,
true_pdf(t),
':',
color='black',
zorder=3,
label="Generating Distribution")
ax.plot(xN, -0.005 * np.ones(len(xN)), '|k')
hist(xN,
# Fetch the great wall data
X = fetch_great_wall()
#------------------------------------------------------------
# Create the grid on which to evaluate the results
Nx = 50
Ny = 125
xmin, xmax = (-375, -175)
ymin, ymax = (-300, 200)
#------------------------------------------------------------
# Evaluate for several models
Xgrid = np.vstack(map(np.ravel, np.meshgrid(np.linspace(xmin, xmax, Nx),
np.linspace(ymin, ymax, Ny)))).T
kde1 = KDE(metric='gaussian', h=5)
dens1 = kde1.fit(X).eval(Xgrid).reshape((Ny, Nx))
kde2 = KDE(metric='tophat', h=5)
dens2 = kde2.fit(X).eval(Xgrid).reshape((Ny, Nx))
kde3 = KDE(metric='exponential', h=5)
dens3 = kde3.fit(X).eval(Xgrid).reshape((Ny, Nx))
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 2.2))
fig.subplots_adjust(left=0.12, right=0.95, bottom=0.2, top=0.9,
hspace=0.01, wspace=0.01)
# First plot: scatter the points