def plot_cdf(sample_count=1000, seed=0):
'''
Plot test statistic cdf based on the Nearest Neighbor distribution [1,2,3].
[1] http://projecteuclid.org/download/pdf_1/euclid.aop/1176993668
[2] http://arxiv.org/pdf/1006.3019v2.pdf
[3] http://en.wikipedia.org/wiki/Nearest_neighbour_distribution
[4] http://en.wikipedia.org/wiki/Volume_of_an_n-ball
'''
seed_all(seed)
fig, (ax1, ax2) = pyplot.subplots(2, 1, sharex=True, figsize=(8, 10))
ax1.plot([0, 1], [0, 1], 'k--')
ax2.plot([0, 1], [1, 1], 'k--')
for model in [nich, lp_nich, niw, lp_niw]:
name = model.__name__.replace('distributions.', '')
name = name.replace('models.', '')
for EXAMPLE in model.EXAMPLES:
dim = get_dim(EXAMPLE['shared']['mu'])
samples, scores = get_samples(model, EXAMPLE, sample_count)
edges = get_edge_stats(samples, scores)
radii = edges['lengths']
intensities = sample_count * numpy.exp(edges['scores'])
cdf = numpy.array([
1 - numpy.exp(-intensity * volume_of_sphere(dim, radius))
for intensity, radius in izip(intensities, radii)
])
cdf.sort()
X = numpy.arange(0.5 / sample_count, 1, 1.0 / sample_count)
pdf, Xp = cdf_to_pdf(cdf, X)
pdf *= sample_count
error = 2 * (sum(cdf) / sample_count) - 1
if abs(error) < 0.05:
status = 'PASS'
linestyle = '-'
else:
status = 'FAIL'
linestyle = '--'
label = '{} {}({}) error = {:.3g}'.format(status, name, dim, error)
ax1.plot(X, cdf, linestyle=linestyle, label=label)
ax2.plot(Xp, pdf, linestyle=linestyle, label=label)
ax1.set_title('GOF of Nearest Neighbor Statistic')
ax1.legend(loc='best', prop={'size': 10}, fancybox=True, framealpha=0.5)
ax1.set_ylabel('CDF')
ax2.set_ylabel('PDF')
pyplot.tight_layout()
fig.subplots_adjust(hspace=0)
pyplot.show()
def plot_cdf(sample_count=1000, seed=0):
'''
Plot test statistic cdf based on the Nearest Neighbor distribution [1,2,3].
[1] http://projecteuclid.org/download/pdf_1/euclid.aop/1176993668
[2] http://arxiv.org/pdf/1006.3019v2.pdf
[3] http://en.wikipedia.org/wiki/Nearest_neighbour_distribution
[4] http://en.wikipedia.org/wiki/Volume_of_an_n-ball
'''
seed_all(seed)
fig, (ax1, ax2) = pyplot.subplots(2, 1, sharex=True, figsize=(8, 10))
ax1.plot([0, 1], [0, 1], 'k--')
ax2.plot([0, 1], [1, 1], 'k--')
for model in [nich, lp_nich, niw, lp_niw]:
name = model.__name__.replace('distributions.', '')
name = name.replace('models.', '')
for EXAMPLE in model.EXAMPLES:
dim = get_dim(EXAMPLE['shared']['mu'])
samples, scores = get_samples(model, EXAMPLE, sample_count)
edges = get_edge_stats(samples, scores)
radii = edges['lengths']
intensities = sample_count * numpy.exp(edges['scores'])
cdf = numpy.array([
1 - numpy.exp(-intensity * volume_of_sphere(dim, radius))
for intensity, radius in izip(intensities, radii)
])
cdf.sort()
X = numpy.arange(0.5 / sample_count, 1, 1.0 / sample_count)
pdf, Xp = cdf_to_pdf(cdf, X)
pdf *= sample_count
error = 2 * (sum(cdf) / sample_count) - 1
if abs(error) < 0.05:
status = 'PASS'
linestyle = '-'
else:
status = 'FAIL'
linestyle = '--'
label = '{} {}({}) error = {:.3g}'.format(status, name, dim, error)
ax1.plot(X, cdf, linestyle=linestyle, label=label)
ax2.plot(Xp, pdf, linestyle=linestyle, label=label)
ax1.set_title('GOF of Nearest Neighbor Statistic')
ax1.legend(loc='best', prop={'size': 10}, fancybox=True, framealpha=0.5)
ax1.set_ylabel('CDF')
ax2.set_ylabel('PDF')
pyplot.tight_layout()
fig.subplots_adjust(hspace=0)
pyplot.show()
def scatter(sample_count=1000, seed=0):
'''
Plot test statistic cdf for all datatpoints in a 2d dataset.
'''
seed_all(seed)
examples = {
(0, 0): get_normal_example,
(1, 0): get_mvn_example,
(0, 1): get_dbg_nich_example,
(1, 1): get_lp_nich_example,
(0, 2): get_dbg_niw_example,
(1, 2): get_lp_niw_example,
}
rows = 1 + max(key[0] for key in examples)
cols = 1 + max(key[1] for key in examples)
fig, axes = pyplot.subplots(rows, cols, figsize=(12, 8))
cmap = pyplot.get_cmap('bwr')
for (row, col), get_example in examples.iteritems():
example = get_example(sample_count)
edges = get_edge_stats(example['samples'], example['scores'])
radii = edges['lengths']
intensities = sample_count * numpy.exp(edges['scores'])
dim = 2
cdf = numpy.array([
1 - numpy.exp(-intensity * volume_of_sphere(dim, radius))
for intensity, radius in izip(intensities, radii)
])
error = 2 * (sum(cdf) / sample_count) - 1
X = [value[0] for value in example['samples']]
Y = [value[1] for value in example['samples']]
colors = cdf
ax = axes[row][col]
ax.set_title('{} error = {:0.3g}'.format(example['name'], error))
ax.scatter(X, Y, 50, alpha=0.5, c=colors, cmap=cmap)
pyplot.tight_layout()
pyplot.show()
def scatter(sample_count=1000, seed=0):
'''
Plot test statistic cdf for all datatpoints in a 2d dataset.
'''
seed_all(seed)
examples = {
(0, 0): get_normal_example,
(1, 0): get_mvn_example,
(0, 1): get_dbg_nich_example,
(1, 1): get_lp_nich_example,
(0, 2): get_dbg_niw_example,
(1, 2): get_lp_niw_example,
}
rows = 1 + max(key[0] for key in examples)
cols = 1 + max(key[1] for key in examples)
fig, axes = pyplot.subplots(rows, cols, figsize=(12, 8))
cmap = pyplot.get_cmap('bwr')
for (row, col), get_example in examples.iteritems():
example = get_example(sample_count)
edges = get_edge_stats(example['samples'], example['scores'])
radii = edges['lengths']
intensities = sample_count * numpy.exp(edges['scores'])
dim = 2
cdf = numpy.array([
1 - numpy.exp(-intensity * volume_of_sphere(dim, radius))
for intensity, radius in izip(intensities, radii)
])
error = 2 * (sum(cdf) / sample_count) - 1
X = [value[0] for value in example['samples']]
Y = [value[1] for value in example['samples']]
colors = cdf
ax = axes[row][col]
ax.set_title('{} error = {:0.3g}'.format(example['name'], error))
ax.scatter(X, Y, 50, alpha=0.5, c=colors, cmap=cmap)
pyplot.tight_layout()
pyplot.show()
def test_volume_of_sphere(self):
for r in [0.1, 1.0, 10.0]:
self.assertAlmostEqual(volume_of_sphere(1, r), 2 * r)
self.assertAlmostEqual(volume_of_sphere(2, r), pi * r ** 2)
self.assertAlmostEqual(volume_of_sphere(3, r), 4 / 3 * pi * r ** 3)
def test_volume_of_sphere(self):
for r in [0.1, 1.0, 10.0]:
self.assertAlmostEqual(volume_of_sphere(1, r), 2 * r)
self.assertAlmostEqual(volume_of_sphere(2, r), pi * r**2)
self.assertAlmostEqual(volume_of_sphere(3, r), 4 / 3 * pi * r**3)
def test_volume_of_sphere():
for r in [0.1, 1.0, 10.0]:
assert_almost_equal(volume_of_sphere(1, r), 2.0 * r)
assert_almost_equal(volume_of_sphere(2, r), pi * r ** 2)
assert_almost_equal(volume_of_sphere(3, r), 4 / 3.0 * pi * r ** 3)
