def test_em_gmm_heterosc(verbose=0):
# testing the model in very ellipsoidal data: compute the big values
# for several values of k and check that the macimal is 1 or 2
# generate some data
dim = 2
x = nr.randn(100, dim)
x[:50, :] += 3
# x[:,0]*=10
# estimate different GMMs of that data
maxiter = 100
delta = 1.0e-4
bic = np.zeros(5)
for k in range(1, 6):
lgmm = GMM(k, dim)
lgmm.initialize(x)
bic[k - 1] = lgmm.estimate(x, maxiter, delta, 0)
if verbose:
print "bic of the %d-classes model" % k, bic
if verbose:
# plot the result
z = lgmm.map_label(x)
from test_bgmm import plot2D
plot2D(x, lgmm, z, show=1, verbose=0)
assert bic[4] < bic[1]
def test_em_gmm_multi(verbose=0):
# Playing with various initilizations on the same data
# generate some data
dim = 2
x = np.concatenate((nr.randn(1000, dim), 3 + 2 * nr.randn(100, dim)))
# estimate different GMMs of that data
maxiter = 100
delta = 1.0e-4
ninit = 5
k = 2
lgmm = GMM(k, dim)
bgmm = lgmm.initialize_and_estimate(x, maxiter, delta, ninit, verbose)
bic = bgmm.evidence(x)
if verbose:
print "bic of the best model", bic
if verbose:
# plot the result
from test_bgmm import plot2D
z = lgmm.map_label(x)
plot2D(x, lgmm, z, show=1, verbose=0)
assert_true(np.isfinite(bic))
def test_em_gmm_largedim(verbose=0):
# testing the GMM model in larger dimensions
# generate some data
dim = 10
x = nr.randn(100, dim)
x[:30, :] += 1
# estimate different GMMs of that data
maxiter = 100
delta = 1.0e-4
for k in range(1, 3):
lgmm = GMM(k, dim)
lgmm.initialize(x)
bic = lgmm.estimate(x, maxiter, delta, verbose)
if verbose:
print "bic of the %d-classes model" % k, bic
z = lgmm.map_label(x)
# define the correct labelling
u = np.zeros(100)
u[:30] = 1
# check the correlation between the true labelling
# and the computed one
eta = np.absolute(np.dot(z - z.mean(), u - u.mean()) / (np.std(z) * np.std(u) * 100))
assert_true(eta > 0.3)
def test_em_gmm_diag(verbose=0):
# Computing the BIC value for GMMs with different number of classes,
# with diagonal covariance models The BIC should maximal for a
# number of classes of 1 or 2
# generate some data
dim = 2
x = np.concatenate((nr.randn(1000, dim), 3 + 2 * nr.randn(1000, dim)))
# estimate different GMMs of that data
maxiter = 100
delta = 1.0e-8
prec_type = "diag"
bic = np.zeros(5)
for k in range(1, 6):
lgmm = GMM(k, dim, prec_type)
lgmm.initialize(x)
bic[k - 1] = lgmm.estimate(x, maxiter, delta, verbose)
if verbose:
print "bic of the %d-classes model" % k, bic
z = lgmm.map_label(x)
assert_true((z.max() + 1 == lgmm.k) & (bic[4] < bic[1]))
def test_em_gmm_largedim(verbose=0):
"""
testing the GMM model in larger dimensions
"""
# generate some data
dim = 10
x = nr.randn(100,dim)
x[:30,:] += 2
# estimate different GMMs of that data
maxiter = 100
delta = 1.e-4
for k in range(2,3):
lgmm = GMM(k,dim)
bgmm = lgmm.initialize_and_estimate(x, None, maxiter, delta, ninit=5)
z = bgmm.map_label(x)
# define the correct labelling
u = np.zeros(100)
u[:30]=1
#check the correlation between the true labelling
# and the computed one
eta = np.absolute(np.dot(z-z.mean(),u-u.mean())/(np.std(z)*np.std(u)*100))
assert (eta>0.3)
def test_em_gmm_full(verbose=0):
# Computing the BIC value for different configurations of a GMM with
# ful diagonal matrices The BIC should be maximal for a number of
# classes of 1 or 2
# generate some data
dim = 2
x = np.concatenate((nr.randn(100, dim), 3 + 2 * nr.randn(100, dim)))
# estimate different GMMs of that data
maxiter = 100
delta = 1.0e-4
bic = np.zeros(5)
for k in range(1, 6):
lgmm = GMM(k, dim)
lgmm.initialize(x)
bic[k - 1] = lgmm.estimate(x, maxiter, delta, verbose)
if verbose:
print "bic of the %d-classes model" % k, bic
z = lgmm.map_label(x)
assert_true(bic[4] < bic[1])
def test_em_loglike1():
dim = 1
k = 3
n = 1000
x = nr.randn(n, dim)
lgmm = GMM(k, dim)
lgmm.initialize(x)
lgmm.estimate(x)
ll = lgmm.average_log_like(x)
ent = 0.5 * (1 + np.log(2 * np.pi))
print ll, ent
assert_true(np.absolute(ll + ent) < 3.0 / np.sqrt(n))
def test_em_loglike4():
dim = 5
k = 1
n = 1000
scale = 3.0
offset = 4.0
x = offset + scale * nr.randn(n, dim)
lgmm = GMM(k, dim)
lgmm.initialize(x)
lgmm.estimate(x)
ll = lgmm.average_log_like(x)
ent = dim * 0.5 * (1 + np.log(2 * np.pi * scale ** 2))
print ll, ent
assert_true(np.absolute(ll + ent) < dim * 3.0 / np.sqrt(n))
def test_em_loglike6():
"""
"""
dim = 1
k = 1
n = 100
offset = 3.
x = nr.randn(n,dim)
y = offset+nr.randn(n,dim)
lgmm = GMM(k,dim)
lgmm.initialize(x)
lgmm.estimate(x)
ll1 = lgmm.average_log_like(x)
ll2 = lgmm.average_log_like(y)
ent = 0.5*(1+np.log(2*np.pi))
dkl = 0.5*offset**2
print ll2, ll1,dkl
assert ll2<ll1
def test_em_loglike2():
"""
"""
dim = 1
k = 1
n = 1000
scale = 3.
offset = 4.
x = offset + scale * nr.randn(n,dim)
lgmm = GMM(k,dim)
lgmm.initialize(x)
lgmm.estimate(x)
ll = lgmm.average_log_like(x)
ent = 0.5*(1+np.log(2*np.pi*scale**2))
print ll, ent
assert np.absolute(ll+ent)<3./np.sqrt(n)
def test_em_gmm_cv(verbose=0):
# Comparison of different GMMs using cross-validation
# generate some data
dim = 2
xtrain = np.concatenate((nr.randn(100, dim), 3 + 2 * nr.randn(100, dim)))
xtest = np.concatenate((nr.randn(1000, dim), 3 + 2 * nr.randn(1000, dim)))
# estimate different GMMs for xtrain, and test it on xtest
prec_type = "full"
k = 2
maxiter = 300
delta = 1.0e-4
ll = []
# model 1
lgmm = GMM(k, dim, prec_type)
lgmm.initialize(xtrain)
bic = lgmm.estimate(xtrain, maxiter, delta)
ll.append(lgmm.test(xtest).mean())
prec_type = "diag"
# model 2
lgmm = GMM(k, dim, prec_type)
lgmm.initialize(xtrain)
bic = lgmm.estimate(xtrain, maxiter, delta)
ll.append(lgmm.test(xtest).mean())
for k in [1, 3, 10]:
lgmm = GMM(k, dim, prec_type)
lgmm.initialize(xtrain)
bic = lgmm.estimate(xtrain, maxiter, delta)
ll.append(lgmm.test(xtest).mean())
assert_true(ll[4] < ll[1])
