def test_imm_loglike_1D_k10():
"""
Chek that the log-likelihood of the data under the
infinite gaussian mixture model
is close to the theortical data likelihood
Here k-fold cross validation is used(k=10)
"""
n = 50
dim = 1
alpha = .5
k = 5
x = np.random.randn(n, dim)
igmm = IMM(alpha, dim)
igmm.set_priors(x)
# warming
igmm.sample(x, niter=100, kfold=k)
# sampling
like = igmm.sample(x, niter=300, kfold=k)
theoretical_ll = -dim*.5*(1+np.log(2*np.pi))
empirical_ll = np.log(like).mean()
print theoretical_ll, empirical_ll
assert np.absolute(theoretical_ll-empirical_ll)<0.25*dim
def test_imm_loglike_2D():
"""
Chek that the log-likelihood of the data under the
infinite gaussian mixture model
is close to the theortical data likelihood
slow (cross-validated) but accurate.
"""
n = 50
dim = 2
alpha = .5
k = 5
x = np.random.randn(n, dim)
igmm = IMM(alpha, dim)
igmm.set_priors(x)
# warming
igmm.sample(x, niter=100, init=True, kfold=k)
# sampling
like = igmm.sample(x, niter=300, kfold=k)
theoretical_ll = -dim*.5*(1+np.log(2*np.pi))
empirical_ll = np.log(like).mean()
print theoretical_ll, empirical_ll
assert np.absolute(theoretical_ll-empirical_ll)<0.25*dim
def test_imm_loglike_known_groups():
"""
Chek that the log-likelihood of the data under the
infinite gaussian mixture model
is close to the theortical data likelihood
"""
n = 50
dim = 1
alpha = .5
x = np.random.randn(n, dim)
igmm = IMM(alpha, dim)
igmm.set_priors(x)
kfold = np.floor(np.random.rand(n)*5).astype(np.int)
# warming
igmm.sample(x, niter=100)
# sampling
like = igmm.sample(x, niter=300, kfold=kfold)
theoretical_ll = -dim*.5*(1+np.log(2*np.pi))
empirical_ll = np.log(like).mean()
print theoretical_ll, empirical_ll
assert np.absolute(theoretical_ll-empirical_ll)<0.25*dim
def test_imm_loglike_2D_a0_1():
"""
Chek that the log-likelihood of the data under the
infinite gaussian mixture model
is close to the theortical data likelihood
the difference is that now alpha=.1
"""
n = 100
dim = 2
alpha = .1
x = np.random.randn(n, dim)
igmm = IMM(alpha, dim)
igmm.set_priors(x)
# warming
igmm.sample(x, niter=100, init=True)
# sampling
like = igmm.sample(x, niter=300)
theoretical_ll = -dim*.5*(1+np.log(2*np.pi))
empirical_ll = np.log(like).mean()
print theoretical_ll, empirical_ll
assert np.absolute(theoretical_ll-empirical_ll)<0.2*dim