def test_covariance(self):
alpha = ones((4,), float64)
d = Dirichlet(alpha)
cv = d.covariance()
self.assertEqual(cv.shape, (4, 4))
self.assertAlmostEqual(cv[0, 0], 1.0 * (1.0 - 1.0 / 4.0) / (4.0 * 5.0))
self.assertAlmostEqual(cv[0, 1], -1 / (4.0 * 4.0 * 5.0))
def test_relative_entropy(self):
alpha = (2.0, 10.0, 1.0, 1.0)
d = Dirichlet(alpha)
pvec = (0.1, 0.2, 0.3, 0.4)
rent = d.mean_relative_entropy(pvec)
vrent = d.variance_relative_entropy(pvec)
low, high = d.interval_relative_entropy(pvec, 0.95)
# print()
# print('> ', rent, vrent, low, high)
# This test can fail randomly, but the precision from a few
# thousand samples is low. Increasing samples, 1000->2000
samples = 2000
sent = zeros((samples,), float64)
for s in range(samples):
post = d.sample()
e = -entropy(post)
for k in range(4):
e += -post[k] * log(pvec[k])
sent[s] = e
sent.sort()
self.assertTrue(abs(sent.mean() - rent) < 4.0 * sqrt(vrent))
self.assertAlmostEqual(sent.std(), sqrt(vrent), 1)
self.assertTrue(abs(low - sent[int(samples * 0.025)]) < 0.2)
self.assertTrue(abs(high - sent[int(samples * 0.975)]) < 0.2)
def test_covariance(self):
alpha = ones((4, ), float64)
d = Dirichlet(alpha)
cv = d.covariance()
self.assertEqual(cv.shape, (4, 4))
self.assertAlmostEqual(cv[0, 0], 1.0 * (1.0 - 1. / 4.0) / (4.0 * 5.0))
self.assertAlmostEqual(cv[0, 1], -1 / (4. * 4. * 5.))
def test_variance_x(self):
alpha = (1.0, 1.0, 1.0, 1.0)
xx = (2.0, 2.0, 2.0, 2.0)
v = Dirichlet(alpha).variance_x(xx)
self.assertAlmostEqual(v, 0.0)
alpha = (1.0, 2.0, 3.0, 4.0)
xx = (2.0, 0.0, 1.0, 10.0)
v = Dirichlet(alpha).variance_x(xx)
def test_mean_x(self):
alpha = (1.0, 2.0, 3.0, 4.0)
xx = (2.0, 2.0, 2.0, 2.0)
m = Dirichlet(alpha).mean_x(xx)
self.assertEqual(m, 2.0)
alpha = (1.0, 1.0, 1.0, 1.0)
xx = (2.0, 3.0, 4.0, 3.0)
m = Dirichlet(alpha).mean_x(xx)
self.assertEqual(m, 3.0)
def test_init(self):
d = Dirichlet((
1,
1,
1,
1,
))
def test_relative_entropy(self):
alpha = (2.0, 10.0, 1.0, 1.0)
d = Dirichlet(alpha)
pvec = (0.1, 0.2, 0.3, 0.4)
rent = d.mean_relative_entropy(pvec)
vrent = d.variance_relative_entropy(pvec)
low, high = d.interval_relative_entropy(pvec, 0.95)
# print()
# print('> ', rent, vrent, low, high)
# This test can fail randomly, but the precision from a few
# thousand samples is low. Increasing samples, 1000->2000
samples = 2000
sent = zeros((samples, ), float64)
for s in range(samples):
post = d.sample()
e = -entropy(post)
for k in range(4):
e += -post[k] * log(pvec[k])
sent[s] = e
sent.sort()
self.assertTrue(abs(sent.mean() - rent) < 4. * sqrt(vrent))
self.assertAlmostEqual(sent.std(), sqrt(vrent), 1)
self.assertTrue(abs(low - sent[int(samples * 0.025)]) < 0.2)
self.assertTrue(abs(high - sent[int(samples * 0.975)]) < 0.2)
def do_test(alpha, samples=1000):
ent = zeros((samples,), float64)
# alpha = ones( ( K,), Float64 ) * A/K
# pt = zeros( (len(alpha) ,), Float64)
d = Dirichlet(alpha)
for s in range(samples):
p = d.sample()
# print(p)
# pt +=p
ent[s] = entropy(p)
# print(pt/samples)
m = mean(ent)
v = var(ent)
dm = d.mean_entropy()
dv = d.variance_entropy()
# print(alpha, ':', m, v, dm, dv)
error = 4.0 * sqrt(v / samples)
self.assertTrue(abs(m - dm) < error)
self.assertTrue(abs(v - dv) < error) # dodgy error estimate
def do_test(alpha, samples=1000):
ent = zeros((samples, ), float64)
# alpha = ones( ( K,), Float64 ) * A/K
# pt = zeros( (len(alpha) ,), Float64)
d = Dirichlet(alpha)
for s in range(samples):
p = d.sample()
# print(p)
# pt +=p
ent[s] = entropy(p)
# print(pt/samples)
m = mean(ent)
v = var(ent)
dm = d.mean_entropy()
dv = d.variance_entropy()
# print(alpha, ':', m, v, dm, dv)
error = 4. * sqrt(v / samples)
self.assertTrue(abs(m - dm) < error)
self.assertTrue(abs(v - dv) < error) # dodgy error estimate
def test_mean(self):
alpha = ones((10,), float64) * 23.0
d = Dirichlet(alpha)
m = d.mean()
self.assertAlmostEqual(m[2], 1.0 / 10)
self.assertAlmostEqual(sum(m), 1.0)
def test_mean(self):
alpha = ones((10, ), float64) * 23.
d = Dirichlet(alpha)
m = d.mean()
self.assertAlmostEqual(m[2], 1. / 10)
self.assertAlmostEqual(sum(m), 1.0)
