# Author: Jake VanderPlas

# License: BSD

# The figure produced by this code is published in the textbook

# "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)

# For more information, see http://astroML.github.com

# To report a bug or issue, use the following forum:

# https://groups.google.com/forum/#!forum/astroml-general

import numpy as np

from matplotlib import pyplot as plt

from scipy import stats

from astroML.density_estimation import KNeighborsDensity

from astroML.plotting import hist

# Scikit-learn 0.14 added sklearn.neighbors.KernelDensity, which is a very

# fast kernel density estimator based on a KD Tree. We'll use this if

# available (and raise a warning if it isn't).

try:

from sklearn.neighbors import KernelDensity

use_sklearn_KDE = True

except:

import warnings

warnings.warn("KDE will be removed in astroML version 0.3. Please "

"upgrade to scikit-learn 0.14+ and use "

"sklearn.neighbors.KernelDensity.", DeprecationWarning)

from astroML.density_estimation import KDE

use_sklearn_KDE = False

#----------------------------------------------------------------------

# This function adjusts matplotlib settings for a uniform feel in the textbook.

# Note that with usetex=True, fonts are rendered with LaTeX. This may

# result in an error if LaTeX is not installed on your system. In that case,

# you can set usetex to False.

from astroML.plotting import setup_text_plots

setup_text_plots(fontsize=8, usetex=True)

#------------------------------------------------------------

# Generate our data: a mix of several Cauchy distributions

# this is the same data used in the Bayesian Blocks figure

np.random.seed(0)

N = 10000

mu_gamma_f = [(5, 1.0, 0.1),

(14, 1.0, 0.1)]

true_pdf = lambda x: sum([f * stats.cauchy(mu, gamma).pdf(x)

for (mu, gamma, f) in mu_gamma_f])

x = np.concatenate([stats.cauchy(mu, gamma).rvs(int(f * N))

for (mu, gamma, f) in mu_gamma_f])

np.random.shuffle(x)

x = x[x > -10]

x = x[x < 30]

#------------------------------------------------------------

# plot the results

fig = plt.figure(figsize=(5, 5))

fig.subplots_adjust(bottom=0.08, top=0.95, right=0.95, hspace=0.1)

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, bins='blocks', ax=ax, normed=True, zorder=1,

histtype='stepfilled', color='k', alpha=0.2,

label="Bayesian Blocks")

ax.plot(t, dens_nbrs, '-', lw=1.5, color='gray', zorder=2,

label="Nearest Neighbors (k=%i)" % k)

ax.plot(t, dens_kde, '-', color='black', zorder=3,

label="Kernel Density (h=0.1)")

# label the plot

ax.text(0.02, 0.95, "%i points" % N, ha='left', va='top',

transform=ax.transAxes)

ax.set_ylabel('$p(x)$')

ax.legend(loc='upper right')

if subplot == 212:

ax.set_xlabel('$x$')

ax.set_xlim(0, 20)

ax.set_ylim(-0.01, 0.4001)

plt.show()