def test_loglikelihood(self):
gsm = GSM(3, 1)
samples = gsm.sample(100000)
# compute entropy analytically
entropy = 0.5 * slogdet(2. * pi * e * gsm.covariance / gsm.scales)[1]
# compare with estimated entropy
self.assertAlmostEqual(entropy, -mean(gsm.loglikelihood(samples)), 1)
def test_loglikelihood(self): gsm = GSM(3, 1) samples = gsm.sample(100000) # compute entropy analytically entropy = 0.5 * slogdet(2. * pi * e * gsm.covariance / gsm.scales)[1] # compare with estimated entropy self.assertAlmostEqual(entropy, -mean(gsm.loglikelihood(samples)), 1)
def test_basics(self): gsm = GSM(3, 5) self.assertTrue(gsm.scales.size, 5) self.assertTrue(gsm.dim, 3) covariance = cov(randn(gsm.dim, 10)) gsm.covariance = covariance self.assertLess(max(abs(gsm.covariance - covariance)), 1e-8)
def test_basics(self):
gsm = GSM(3, 5)
self.assertTrue(gsm.scales.size, 5)
self.assertTrue(gsm.dim, 3)
covariance = cov(randn(gsm.dim, 10))
gsm.covariance = covariance
self.assertLess(max(abs(gsm.covariance - covariance)), 1e-8)
def test_pickle(self):
models = [
Mixture(dim=5),
MoGSM(dim=3, num_components=4, num_scales=7)]
for _ in range(3):
models[0].add_component(GSM(models[0].dim, 7))
for model0 in models:
tmp_file = mkstemp()[1]
# store model
with open(tmp_file, 'w') as handle:
dump({'model': model0}, handle)
# load model
with open(tmp_file) as handle:
model1 = load(handle)['model']
# make sure parameters haven't changed
self.assertEqual(model0.dim, model1.dim)
self.assertEqual(model0.num_components, model1.num_components)
for k in range(model0.num_components):
self.assertLess(max(abs(model0[k].scales - model0[k].scales)), 1e-10)
self.assertLess(max(abs(model0[k].priors - model1[k].priors)), 1e-10)
self.assertLess(max(abs(model0[k].mean - model1[k].mean)), 1e-10)
self.assertLess(max(abs(model0[k].covariance - model1[k].covariance)), 1e-10)
def test_train(self):
model = Mixture(3)
model.add_component(GSM(3, 1))
model.add_component(GSM(3, 1))
self.assertRaises(Exception, model.add_component, GSM(5))
self.assertRaises(Exception, model.__getitem__, 2)
self.assertIsInstance(model[1], GSM)
p0 = 0.3
p1 = 0.7
N = 20000
m0 = array([[2], [0], [0]])
m1 = array([[0], [2], [1]])
C0 = cov(randn(model.dim, model.dim**2))
C1 = cov(randn(model.dim, model.dim**2))
data = hstack([
dot(cholesky(C0), randn(model.dim, int(p0 * N))) + m0,
dot(cholesky(C1), randn(model.dim, int(p1 * N))) + m1])
# if this is not call train() will initialize the parameters
model.initialize(data)
model[0].mean = m0
model[1].mean = m1
model[0].covariance = C0
model[1].covariance = C1
model[0].scales = [1.]
model[1].scales = [1.]
# training shouldn't change the parameters too much
model.train(data, parameters={'verbosity': 0, 'max_iter': 20, 'threshold': 1e-7})
self.assertLess(abs(1. - model.priors[0] / p0), 0.1)
self.assertLess(abs(1. - model.priors[1] / p1), 0.1)
self.assertLess(max(abs(model[0].mean - m0)), 0.2)
self.assertLess(max(abs(model[1].mean - m1)), 0.2)
self.assertLess(max(abs(model[0].covariance / model[0].scales - C0)), 0.2)
self.assertLess(max(abs(model[1].covariance / model[1].scales - C1)), 0.2)
def test_pickle(self):
model0 = GSM(7, 9)
model0.mean = randn(7, 1)
model0.covariance = cov(randn(7, 20))
tmp_file = mkstemp()[1]
# store model
with open(tmp_file, 'w') as handle:
dump({'model': model0}, handle)
# load model
with open(tmp_file) as handle:
model1 = load(handle)['model']
# make sure parameters haven't changed
self.assertEqual(model0.dim, model1.dim)
self.assertEqual(model0.num_scales, model1.num_scales)
self.assertLess(max(abs(model0.scales - model0.scales)), 1e-10)
self.assertLess(max(abs(model0.priors - model1.priors)), 1e-10)
self.assertLess(max(abs(model0.mean - model1.mean)), 1e-10)
self.assertLess(max(abs(model0.covariance - model1.covariance)), 1e-10)
def test_pickle(self):
model0 = GSM(7, 9)
model0.mean = randn(7, 1)
model0.covariance = cov(randn(7, 20))
tmp_file = mkstemp()[1]
# store model
with open(tmp_file, 'w') as handle:
dump({'model': model0}, handle)
# load model
with open(tmp_file) as handle:
model1 = load(handle)['model']
# make sure parameters haven't changed
self.assertEqual(model0.dim, model1.dim)
self.assertEqual(model0.num_scales, model1.num_scales)
self.assertLess(max(abs(model0.scales - model0.scales)), 1e-10)
self.assertLess(max(abs(model0.priors - model1.priors)), 1e-10)
self.assertLess(max(abs(model0.mean - model1.mean)), 1e-10)
self.assertLess(max(abs(model0.covariance - model1.covariance)), 1e-10)
def test_train(self):
gsm0 = GSM(3, 2)
gsm0.mean = [1, 1, 1]
gsm0.scales = [1, 5]
gsm0.priors = [0.7, 0.3]
gsm0.covariance = gsm0.covariance / power(det(gsm0.covariance), 1. / gsm0.dim)
samples = gsm0.sample(50000)
# try to recover parameters
gsm1 = GSM(3, 2)
gsm1.train(samples, parameters={'max_iter': 50})
# normalize
f = power(det(gsm1.covariance), 1. / gsm1.dim)
gsm1.covariance = gsm1.covariance / f
gsm1.scales = gsm1.scales / f
self.assertLess(max(abs(gsm1.mean - gsm0.mean)), 0.2)
self.assertLess(max(abs(1. - sort(gsm1.priors.ravel()) / sort(gsm0.priors.ravel()))), 0.2)
self.assertLess(max(abs(1. - sort(gsm1.scales.ravel()) / sort(gsm0.scales.ravel()))), 0.2)
self.assertLess(max(abs(gsm1.covariance - gsm0.covariance)), 0.2)
weights = rand(1, samples.shape[1])
weights /= sum(weights)
gsm1 = GSM(3, 2)
gsm1.train(samples, weights=weights, parameters={'max_iter': 100})
# normalize
f = power(det(gsm1.covariance), 1. / gsm1.dim)
gsm1.covariance = gsm1.covariance / f
gsm1.scales = gsm1.scales / f
self.assertLess(max(abs(gsm1.mean - gsm0.mean)), 0.2)
self.assertLess(max(abs(1. - sort(gsm1.priors.ravel()) / sort(gsm0.priors.ravel()))), 0.2)
self.assertLess(max(abs(1. - sort(gsm1.scales.ravel()) / sort(gsm0.scales.ravel()))), 0.2)
self.assertLess(max(abs(gsm1.covariance - gsm0.covariance)), 0.2)
def test_train(self):
gsm0 = GSM(3, 2)
gsm0.mean = [1, 1, 1]
gsm0.scales = [1, 5]
gsm0.priors = [0.7, 0.3]
gsm0.covariance = gsm0.covariance / power(det(gsm0.covariance),
1. / gsm0.dim)
samples = gsm0.sample(50000)
# try to recover parameters
gsm1 = GSM(3, 2)
gsm1.train(samples, parameters={'max_iter': 50})
# normalize
f = power(det(gsm1.covariance), 1. / gsm1.dim)
gsm1.covariance = gsm1.covariance / f
gsm1.scales = gsm1.scales / f
self.assertLess(max(abs(gsm1.mean - gsm0.mean)), 0.2)
self.assertLess(
max(abs(1. -
sort(gsm1.priors.ravel()) / sort(gsm0.priors.ravel()))),
0.2)
self.assertLess(
max(abs(1. -
sort(gsm1.scales.ravel()) / sort(gsm0.scales.ravel()))),
0.2)
self.assertLess(max(abs(gsm1.covariance - gsm0.covariance)), 0.2)
weights = rand(1, samples.shape[1])
weights /= sum(weights)
gsm1 = GSM(3, 2)
gsm1.train(samples, weights=weights, parameters={'max_iter': 100})
# normalize
f = power(det(gsm1.covariance), 1. / gsm1.dim)
gsm1.covariance = gsm1.covariance / f
gsm1.scales = gsm1.scales / f
self.assertLess(max(abs(gsm1.mean - gsm0.mean)), 0.2)
self.assertLess(
max(abs(1. -
sort(gsm1.priors.ravel()) / sort(gsm0.priors.ravel()))),
0.2)
self.assertLess(
max(abs(1. -
sort(gsm1.scales.ravel()) / sort(gsm0.scales.ravel()))),
0.2)
self.assertLess(max(abs(gsm1.covariance - gsm0.covariance)), 0.2)